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CATEGORY:
Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020)
[back]

TOPIC: Noisy Machines by Michael James Kewming [refresh]

TOPIC: Noisy Machines by Michael James Kewming [refresh]

The abstract notion of a Universal Turing machine cannot exist as a physical subsystem without the introduction of noise from an external energy source. The mathematical paradoxes uncovered by Turing and Godel do not bear any consequence on physical world because they can never be truly realised in physics. Like many other mathematical anomalies arising in the realm of Platonic forms, they are denied a physical existence by the laws of thermodynamics.

Michael Kewming is a PhD student in the School of Mathematics and Physics at the University of Queensland, Australia. His research relates to experimental quantum optics and the theoretical study of open quantum systems.

"In the world of finite systems, nature will always force a solution to the Halting problem because nature does not permit contradictions: The asymptotic predictions of closed axiomatic systems can never exist in the physical world." What empirical evidence supports the preceding idea? What are the arguments against the following?

The Seven Sagacities of String Theory with the Finite Nature Hypothesis: (1) There is a profound synergy between string theory with the infinite nature hypothesis and string theory with the finite nature hypothesis. (2) Milgrom is the Kepler of contemporary cosmology — on the basis of overwhelming empirical evidence (implying dark-matter-compensation-constant = (3.9±.5) * 10^–5). (3) The Koide formula is essential for understanding the foundations of physics. (4) Lestone's theory of virtual cross sections is essential for understanding the foundations of physics. (5) The idea of Fernández-Rañada and Tiemblo-Ramos that atomic time is different from astronomical time is correct. (6) There is genius in the ideas of Riofrio, Sanejouand, and Pipino concerning the hypothesis that the speed of light in a perfect vacuum steadily decreases as our universe ages. (7) Quantum information reduces to Fredkin-Wolfram information, which is controlled by Wolfram's cosmological automaton in a mathematical structure isomorphic to a 72-dimensional, holographic, digital computer.

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The Seven Sagacities of String Theory with the Finite Nature Hypothesis: (1) There is a profound synergy between string theory with the infinite nature hypothesis and string theory with the finite nature hypothesis. (2) Milgrom is the Kepler of contemporary cosmology — on the basis of overwhelming empirical evidence (implying dark-matter-compensation-constant = (3.9±.5) * 10^–5). (3) The Koide formula is essential for understanding the foundations of physics. (4) Lestone's theory of virtual cross sections is essential for understanding the foundations of physics. (5) The idea of Fernández-Rañada and Tiemblo-Ramos that atomic time is different from astronomical time is correct. (6) There is genius in the ideas of Riofrio, Sanejouand, and Pipino concerning the hypothesis that the speed of light in a perfect vacuum steadily decreases as our universe ages. (7) Quantum information reduces to Fredkin-Wolfram information, which is controlled by Wolfram's cosmological automaton in a mathematical structure isomorphic to a 72-dimensional, holographic, digital computer.

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Dear Michael Kewming,

Considering the perhaps “uncompromising” position you took, you make a rather persuasive essay.

You write

“If the external world is to be the source of energy, then doing the abstract task of mathematics still requires we model the whole process as intrinsically irreversible.”

But I ask, what happens then to the thermodynamics notion that the universe as a whole will resemble an isolated system? And what happens to the idealized notion of a blackbody cavity as a**unit** emissivity and unit absorptance, from which in the first place we have extracted the quantum theory?

I would think that thermodynamics does not check mathematics. On the contrary, thermodynamics only approximates mathematics. Just as real gases only approximate the ideal gas.

These considerations lead me, personally, to the proposal that modelling the observer proper as being a part of the same system of waves it is trying to measure/describe makes it physically the**de facto** self-referencing state of Gödel’s theorem and, therefore own undecidable information.

Now this must be equivalent physically to modelling the observer as own de facto Heisenberg uncertainty (indeed own de facto quantum of observables). In other words, the observer as opposed to the observable or “information” is actually by definition own Landauer limit.

In my essay I try to show that the mind (sensory threshold) in man actually qualifies as the Landauer limit and that this makes the mind own bona fide natural unit of momentum a.k.a. the matter wave p = kħ.

I would love to take your questions (and please don’t let any poor wordings distract you).

Chidi Idika (forum topic: 3531)

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Considering the perhaps “uncompromising” position you took, you make a rather persuasive essay.

You write

“If the external world is to be the source of energy, then doing the abstract task of mathematics still requires we model the whole process as intrinsically irreversible.”

But I ask, what happens then to the thermodynamics notion that the universe as a whole will resemble an isolated system? And what happens to the idealized notion of a blackbody cavity as a

I would think that thermodynamics does not check mathematics. On the contrary, thermodynamics only approximates mathematics. Just as real gases only approximate the ideal gas.

These considerations lead me, personally, to the proposal that modelling the observer proper as being a part of the same system of waves it is trying to measure/describe makes it physically the

Now this must be equivalent physically to modelling the observer as own de facto Heisenberg uncertainty (indeed own de facto quantum of observables). In other words, the observer as opposed to the observable or “information” is actually by definition own Landauer limit.

In my essay I try to show that the mind (sensory threshold) in man actually qualifies as the Landauer limit and that this makes the mind own bona fide natural unit of momentum a.k.a. the matter wave p = kħ.

I would love to take your questions (and please don’t let any poor wordings distract you).

Chidi Idika (forum topic: 3531)

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i'm unable to follow all the arguments exposed still i like that you mention heat emission for components, and noise

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Really wonderful essay, great work! It was full of some beautiful, lively turns of phrase. Some of my favorites: "big bang buzzes"; "marble edifice contained cracks"; "Platonic divide"; "vectors, perfection, and infinity"; "swinging bridge between the abstract and mechanical"; "unalterable march of the second law of thermodynamics"; and "canvas of spacetime".

I like your point about the futility of attempting to circumvent computational errors due to noise: needing error-correcting Turing machines to error-correct their error correcters feels like turtles all the way down. You need to constantly pump in energy and be correcting errors to be confident that your calculations are right, but the errors still creep in eventually...

We seemed to think along similar lines on many topics, e.g. the limited computational capacity of the universe (you also cited Lloyd), the omnipresence of uncertainty, and the importance of coarse-graining for understanding anything about the world. So I'm largely sympathetic to the views you expressed in your essay.

A couple questions. Wasn't sure from the essay: do you view mathematics as not living in some Platonic realm, out of space and time? It seemed like you thought about it as requiring physical context. Also, I'm skeptical of invoking the second law of thermodynamics, since it and the idea of irreversibility are very much emergent. Do you think there's a universe (or branch of the wave function of our universe, maybe) where everything conspires just right for a Turing machine to not heat up or require error correction, allowing it to run indefinitely? Obviously it would be extraordinarily unlikely, but do you think it's possible in principle?

P.S. Hope you keep writing essays like these. Again, I really enjoyed reading it, and I think you've got a talent for it.

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I like your point about the futility of attempting to circumvent computational errors due to noise: needing error-correcting Turing machines to error-correct their error correcters feels like turtles all the way down. You need to constantly pump in energy and be correcting errors to be confident that your calculations are right, but the errors still creep in eventually...

We seemed to think along similar lines on many topics, e.g. the limited computational capacity of the universe (you also cited Lloyd), the omnipresence of uncertainty, and the importance of coarse-graining for understanding anything about the world. So I'm largely sympathetic to the views you expressed in your essay.

A couple questions. Wasn't sure from the essay: do you view mathematics as not living in some Platonic realm, out of space and time? It seemed like you thought about it as requiring physical context. Also, I'm skeptical of invoking the second law of thermodynamics, since it and the idea of irreversibility are very much emergent. Do you think there's a universe (or branch of the wave function of our universe, maybe) where everything conspires just right for a Turing machine to not heat up or require error correction, allowing it to run indefinitely? Obviously it would be extraordinarily unlikely, but do you think it's possible in principle?

P.S. Hope you keep writing essays like these. Again, I really enjoyed reading it, and I think you've got a talent for it.

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Thanks for the kind words John :)

In response to your question, I would honestly answer with; I don't know. Given the infinite nature of say, real numbers, it doesn't seem like they are physical. But in saying this, we humans with our mushy brains are finite creatures which dreamed up mathematics, hence why I drew on Landauer's work so much: He would argue mathematics must be bounded by physical constraints for this reason. Therefore, is it possible to bridge these two? I argued that if real Turing machine are an attempt to physically realise mathematics, but because of thermodynamics and the energy requirements to run the thing, you still can't realise all of mathematics i.e the halting problem. Thus, a Turing machine cannot be a viable way to bridge this Platonic divide.

For the wavefunction to evolve via the schrodinger equation, we need some potential energy V(t). Typically, we just add V(t) to our calculation without really asking where it comes from. In reality, it comes via the interaction of your system to an external environment i.e light matter interaction and the dipole moment. Now we can always include this entire interaction ad infinitum in our system, but we are now running with open arms into the church of the higher hilbert space. I'd argue that if your trying to build a Turing machine, eventually, there is going to be some interaction that you just can't as it's lost in the soup. At this point, errors are going to creep in and thermodynamics comes into the fray.

I completely understand the sympathy of your scepticism about hinging my arguments on thermodynamics since it is emergent. But if mathematics is Platonic and only in our heads, then it to must be emergent. I don't believe our brains hit some critical mass which allowed opened up a portal to the Platonic realm: For me, such an argument is necessarily on par with the claim that one can speak to God through prayer.

Again, thanks for taking the time for reading my essay!

In response to your question, I would honestly answer with; I don't know. Given the infinite nature of say, real numbers, it doesn't seem like they are physical. But in saying this, we humans with our mushy brains are finite creatures which dreamed up mathematics, hence why I drew on Landauer's work so much: He would argue mathematics must be bounded by physical constraints for this reason. Therefore, is it possible to bridge these two? I argued that if real Turing machine are an attempt to physically realise mathematics, but because of thermodynamics and the energy requirements to run the thing, you still can't realise all of mathematics i.e the halting problem. Thus, a Turing machine cannot be a viable way to bridge this Platonic divide.

For the wavefunction to evolve via the schrodinger equation, we need some potential energy V(t). Typically, we just add V(t) to our calculation without really asking where it comes from. In reality, it comes via the interaction of your system to an external environment i.e light matter interaction and the dipole moment. Now we can always include this entire interaction ad infinitum in our system, but we are now running with open arms into the church of the higher hilbert space. I'd argue that if your trying to build a Turing machine, eventually, there is going to be some interaction that you just can't as it's lost in the soup. At this point, errors are going to creep in and thermodynamics comes into the fray.

I completely understand the sympathy of your scepticism about hinging my arguments on thermodynamics since it is emergent. But if mathematics is Platonic and only in our heads, then it to must be emergent. I don't believe our brains hit some critical mass which allowed opened up a portal to the Platonic realm: For me, such an argument is necessarily on par with the claim that one can speak to God through prayer.

Again, thanks for taking the time for reading my essay!

Dear Michael,

thank you for an excellent essay, very clear and well-argued. As you have firstly noticed, there are many elements of resonance between our ideas. I particularly appreciated how you managed to draw a line between abstract mathematics and physical processes, a way of operationalising maths. It's insightful also your discussion on the limit of infinite processes due to the kick in of a sort of thermodynamica obsolescence. This led you to a great conclusion: "Deterministic

theories like a microscope, focus down on a highly specific piece of nature by closing out the rest of reality".

(Please also have a look at my reply to your post on my essay's page).

Congrats again on a very good piece of work, to which I gave full points! And good luck for the contest.

All good wishesm

Flavio

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thank you for an excellent essay, very clear and well-argued. As you have firstly noticed, there are many elements of resonance between our ideas. I particularly appreciated how you managed to draw a line between abstract mathematics and physical processes, a way of operationalising maths. It's insightful also your discussion on the limit of infinite processes due to the kick in of a sort of thermodynamica obsolescence. This led you to a great conclusion: "Deterministic

theories like a microscope, focus down on a highly specific piece of nature by closing out the rest of reality".

(Please also have a look at my reply to your post on my essay's page).

Congrats again on a very good piece of work, to which I gave full points! And good luck for the contest.

All good wishesm

Flavio

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Hi Flavio,

Thanks for taking a look at my essay and the full points! :)

As you pointed out in your response in your thread, there is several interesting points of overlap between our ideas.

Cheers,

Michael

Thanks for taking a look at my essay and the full points! :)

As you pointed out in your response in your thread, there is several interesting points of overlap between our ideas.

Cheers,

Michael

Dear Michael,

Congratulations for your well written and interesting essay.

Your conclusion : " The processing logic of error-correction must come from an external processing unit also sourcing its power from the environment. By implication, the physical realisation of indefinite self-referential logical program such as the Halting problem relies on an external network of other external logical processors to prevent errors." is really appealing to me, as this is quite analog to my idea that self-referential issues inside quantum theory can be dissolved by invoking an "external object", an observer, and thus the measurement problem is just a logical tension between physics-from-inside and physics-from-outside.

However, I am not sure to follow you when you write that "the mathematical paradoxes uncovered by Turing and Gödel do not bear any consequence on the physical world because they can never be truly realised in physics." Or at least, they have a huge importance in meta-physics...

All the best,

Hippolyte

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Congratulations for your well written and interesting essay.

Your conclusion : " The processing logic of error-correction must come from an external processing unit also sourcing its power from the environment. By implication, the physical realisation of indefinite self-referential logical program such as the Halting problem relies on an external network of other external logical processors to prevent errors." is really appealing to me, as this is quite analog to my idea that self-referential issues inside quantum theory can be dissolved by invoking an "external object", an observer, and thus the measurement problem is just a logical tension between physics-from-inside and physics-from-outside.

However, I am not sure to follow you when you write that "the mathematical paradoxes uncovered by Turing and Gödel do not bear any consequence on the physical world because they can never be truly realised in physics." Or at least, they have a huge importance in meta-physics...

All the best,

Hippolyte

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Hi Hippolyte,

Thanks for taking a look at my essay.

Yes I agree that they have importance from metaphysics and mathematics but any attempt to execute them physically is impossible.

We can do the abstract task of metaphysics but this---currently---appears to be orthogonal to physics i.e we can discuss perpetual motion machines but we can't make them, thus any machine that relies on perpetual motion machine cannot be realised either. Likewise, Halting problems and mathematical anomalies can't be made in physics.

Now, this is not to say they can't be conceptually useful, but they are certainly not physical. Therefore any physical model that relies on them is somewhat meaningless; but this is not true for metaphysical models.

I hope this clears up what I meant.

Michael

Thanks for taking a look at my essay.

Yes I agree that they have importance from metaphysics and mathematics but any attempt to execute them physically is impossible.

We can do the abstract task of metaphysics but this---currently---appears to be orthogonal to physics i.e we can discuss perpetual motion machines but we can't make them, thus any machine that relies on perpetual motion machine cannot be realised either. Likewise, Halting problems and mathematical anomalies can't be made in physics.

Now, this is not to say they can't be conceptually useful, but they are certainly not physical. Therefore any physical model that relies on them is somewhat meaningless; but this is not true for metaphysical models.

I hope this clears up what I meant.

Michael

Hi Michael,

I enjoyed your essay, you write very well, your explanations are clear, and you made very interesting points. I must agree with you, noise is ubiquitous, and it's not always a bad thing. Without it we couldn't exist. I wish you good luck with the essay!

Cheers,

Cristi

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I enjoyed your essay, you write very well, your explanations are clear, and you made very interesting points. I must agree with you, noise is ubiquitous, and it's not always a bad thing. Without it we couldn't exist. I wish you good luck with the essay!

Cheers,

Cristi

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Hi Michael!

This is a fantastic essay! I really love how you talked about the physical nature of Turing machines, I think something that is often overlooked. I think the Church-Turing thesis is very deep, but also unfortunately allowed people to think about computation in such an abstract sense, that we forgot about the physical needs to perform computations! So thank you for bringing this to attention.

Do you think that, because of the above, it is more useful to think of computation in terms of lambda calculus? I think Lamba calculus is useful since it does not make the distinction between data and programs, which is explicitly distinct in Turing's language of combustion. Actually I think this is an extremely powerful viewpoint when thinking about biology, and so it makes me wonder why there isn't more work in understanding the physical thermodynamics of Turing machines and their equivalent lambda functions. Landaur's principle helps a little, but I haven't found a nice way to see a Turing machine and calculate its potential energy from its look-up table.

I'm curious to know what you think!

Cheers!

Alyssa

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This is a fantastic essay! I really love how you talked about the physical nature of Turing machines, I think something that is often overlooked. I think the Church-Turing thesis is very deep, but also unfortunately allowed people to think about computation in such an abstract sense, that we forgot about the physical needs to perform computations! So thank you for bringing this to attention.

Do you think that, because of the above, it is more useful to think of computation in terms of lambda calculus? I think Lamba calculus is useful since it does not make the distinction between data and programs, which is explicitly distinct in Turing's language of combustion. Actually I think this is an extremely powerful viewpoint when thinking about biology, and so it makes me wonder why there isn't more work in understanding the physical thermodynamics of Turing machines and their equivalent lambda functions. Landaur's principle helps a little, but I haven't found a nice way to see a Turing machine and calculate its potential energy from its look-up table.

I'm curious to know what you think!

Cheers!

Alyssa

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Hi Alyssa,

Thank you for suggesting Lambda calculus, I think it would be a really interesting avenue to pursue! Personally I haven't put much thought into it, but as a guess, I would suppose it would be subject to similar constraints. The operations of any information processing framework can be done without an increase in entropy, however it is the encoding/decoding side which is irreversible.

Encoding any information in a physical structure is intrinsically dissapative---provided you don't keep track of all the absurd amount entanglement being generated between subsystems. Biological/genetic systems exhibit a huge amount dissipation and heat generation which down at the smallest scale must be closely bound by Landaur's principle. Although it might not be the processing that is dissapative but the transmission reading/writing side that is generating heat.

To be honest, I'm being very speculative but I think I will certainly dig into lambda calculus more. Thank you for the suggestion!

Michael

Thank you for suggesting Lambda calculus, I think it would be a really interesting avenue to pursue! Personally I haven't put much thought into it, but as a guess, I would suppose it would be subject to similar constraints. The operations of any information processing framework can be done without an increase in entropy, however it is the encoding/decoding side which is irreversible.

Encoding any information in a physical structure is intrinsically dissapative---provided you don't keep track of all the absurd amount entanglement being generated between subsystems. Biological/genetic systems exhibit a huge amount dissipation and heat generation which down at the smallest scale must be closely bound by Landaur's principle. Although it might not be the processing that is dissapative but the transmission reading/writing side that is generating heat.

To be honest, I'm being very speculative but I think I will certainly dig into lambda calculus more. Thank you for the suggestion!

Michael

Hi Michael,

This is wonderful essay and opens the big picture on "computational machine". In my past essay, which was finally published as the book chapter, informational context and computation in terms of Maxwell's demon have already been discussed.

In your essay, I do not understand the connection between thermodynamic context and quantum reality except for the*irreversiblity*. From computational viewpoint, do you think to open a new pathway to understand this connection?

On the reference [11], Roger Penrose is not the author but was communicated with.

Best wishes,

Yutaka

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This is wonderful essay and opens the big picture on "computational machine". In my past essay, which was finally published as the book chapter, informational context and computation in terms of Maxwell's demon have already been discussed.

In your essay, I do not understand the connection between thermodynamic context and quantum reality except for the

On the reference [11], Roger Penrose is not the author but was communicated with.

Best wishes,

Yutaka

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Hi Yutuka,

Thank you for the kind words (and pointing out the reference error).

In the Quantum reality section I was arguing that even the Church-Turing-Deutsch principle is still subject to the same irreversible constraints arising from encoding/decoding information in physical subsystems. While the underlying hardware and processing capabilities between classical and quantum computers is fundamentally different, the process of reading and writing will introduce noise in the exact same way for both. In this sense, a quantum computer is subject to same thermodynamic constraints as a classical computer and cannot realise an undecidable problem.

I hope this clears up my intent!

Thanks again for taking the time to look at my essay.

Michael

Thank you for the kind words (and pointing out the reference error).

In the Quantum reality section I was arguing that even the Church-Turing-Deutsch principle is still subject to the same irreversible constraints arising from encoding/decoding information in physical subsystems. While the underlying hardware and processing capabilities between classical and quantum computers is fundamentally different, the process of reading and writing will introduce noise in the exact same way for both. In this sense, a quantum computer is subject to same thermodynamic constraints as a classical computer and cannot realise an undecidable problem.

I hope this clears up my intent!

Thanks again for taking the time to look at my essay.

Michael

Dear Michael,

It’s very kind of you to read my essay and comment on it, thanks so much, as it has led me to your well crafted and most enjoyable essay, which I will give a very good rating.

As a practicing physicist measuring magnetic fields I deal with noise on a daily basis. As a hobbyist radio-astronomer noise is our bread and butter. As a retired EMC practitioner noise was...

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It’s very kind of you to read my essay and comment on it, thanks so much, as it has led me to your well crafted and most enjoyable essay, which I will give a very good rating.

As a practicing physicist measuring magnetic fields I deal with noise on a daily basis. As a hobbyist radio-astronomer noise is our bread and butter. As a retired EMC practitioner noise was...

view entire post

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Hi Lachlan,

Thank you for the kind words. Yes, noise is ubiquitous and it's always a central concern as an experimentalist.

You have a lot of big challenges with QM as you list. Personally, I would subscribe to the argument that if observed reality cannot be explained by factorising the observed statistics in probability distributions over hidden variables, then it cannot be explained by a classical theory.

However, there is still certainly room to move since we still haven't reconciled the tension between locality and realism, nor have we brought gravity fully into the fray (or dark matter on that note), so it is hard to put QM on a complete description of reality of pedestal as you claim. For the time being I would submit that QM in its current form is incredibly useful and explains a huge chunk of observations, but is it the full picture? Certainly not.

Anyways, thanks again for taking the time to read my essay! Good luck in the competition.

Michael

Thank you for the kind words. Yes, noise is ubiquitous and it's always a central concern as an experimentalist.

You have a lot of big challenges with QM as you list. Personally, I would subscribe to the argument that if observed reality cannot be explained by factorising the observed statistics in probability distributions over hidden variables, then it cannot be explained by a classical theory.

However, there is still certainly room to move since we still haven't reconciled the tension between locality and realism, nor have we brought gravity fully into the fray (or dark matter on that note), so it is hard to put QM on a complete description of reality of pedestal as you claim. For the time being I would submit that QM in its current form is incredibly useful and explains a huge chunk of observations, but is it the full picture? Certainly not.

Anyways, thanks again for taking the time to read my essay! Good luck in the competition.

Michael

Dear Michal James.

"MEMORY" is just a time-effect in our emergent reality. (so it originates from a Point in a Point of TS).

I will read your essay, I promise, but today I am hospitalized for an operation on my colon where they will take away a tumour. I will have to stay ca 12 days before coming home.

best regards

Wilhelmus

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"MEMORY" is just a time-effect in our emergent reality. (so it originates from a Point in a Point of TS).

I will read your essay, I promise, but today I am hospitalized for an operation on my colon where they will take away a tumour. I will have to stay ca 12 days before coming home.

best regards

Wilhelmus

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Dear Michael,

you've provided a well-argued essay that takes the abstract notions of 'austere' mathematical Platonic domains and confronts them with the hands-on reality of the actual world. Do the issues noted by Gödel, Turing, and others survive the confrontation with a messy, noisy world of increasing entropy and finite resources?

You answer in the negative---and in the way you...

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you've provided a well-argued essay that takes the abstract notions of 'austere' mathematical Platonic domains and confronts them with the hands-on reality of the actual world. Do the issues noted by Gödel, Turing, and others survive the confrontation with a messy, noisy world of increasing entropy and finite resources?

You answer in the negative---and in the way you...

view entire post

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Hi Jochen,

Thanks for the feedback! You raise some very good points and I will do my best to try and answer them all.

I agree that the notions of undeciability and uncomputability can be extremely useful tools and essential for formulating theories and laws of nature. This gives us incredible power to make predictions and derive some intuitions about our reality, but at the end of...

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Thanks for the feedback! You raise some very good points and I will do my best to try and answer them all.

I agree that the notions of undeciability and uncomputability can be extremely useful tools and essential for formulating theories and laws of nature. This gives us incredible power to make predictions and derive some intuitions about our reality, but at the end of...

view entire post

Dear Michael,

Thank you for steering me to your great essay. Kudos to you for asserting the fundamental inevitability of noise from the environment. You brilliantly capture the impossibility of isolating it by your statements: “The afterglow of the big bang buzzes in the background and virtual particles pop in and out of existence. No matter where you are in the universe, you cannot...

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Thank you for steering me to your great essay. Kudos to you for asserting the fundamental inevitability of noise from the environment. You brilliantly capture the impossibility of isolating it by your statements: “The afterglow of the big bang buzzes in the background and virtual particles pop in and out of existence. No matter where you are in the universe, you cannot...

view entire post

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Dear Michael,

This is very nice and well argued essay you have proposed here. I learnt many things, I did not know about conservative logic for example, and will for sure come back to it multiple times in the coming months.

You are perfectly correct that noise should not, and maybe cannot, be discarded. And the reference to the 3 Kelvin CMB is pot on about this.

A small issue I have with one of the theses you develop however, is that you say that because a computer ultimately relies on external resources (whatever they are for: memory, energy etc...), once this storage somehow runs out the programme will halt. This is perfectly true but I would not consider this as being the same as saying that the halting problem does not apply. If the programme is terminated before it terminates on its own then it is still a major problem and this is not, I believe, what the original Halting problem was about.

So, to me, if anything, you actually put forward, like Paul Davies does in his essay, an additional limitation to computation.

So, instead of dispelling these undecidability and incompatibility problems, I think you actually add to them by considering more realistic scenarios.

Another interesting point you mention is that mathematics can only go as far as the tools of mathematics, themselves governed by the laws of physics, enable them to go.

I would venture to object that the very laws of physics we have developed are equally prone to the same critic. So I am not sure how one can be used to undermine the other.

This reminds me of Penrose's claim that the proof of Godel's first incompleteness theorem could not be checked by a Turing machine and out of which he would conclude that our brains go beyond such idealised machines. Do you have any thoughts about this?

Many thanks again for this inspiring essay.

Best of luck for the contest.

Fabien

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This is very nice and well argued essay you have proposed here. I learnt many things, I did not know about conservative logic for example, and will for sure come back to it multiple times in the coming months.

You are perfectly correct that noise should not, and maybe cannot, be discarded. And the reference to the 3 Kelvin CMB is pot on about this.

A small issue I have with one of the theses you develop however, is that you say that because a computer ultimately relies on external resources (whatever they are for: memory, energy etc...), once this storage somehow runs out the programme will halt. This is perfectly true but I would not consider this as being the same as saying that the halting problem does not apply. If the programme is terminated before it terminates on its own then it is still a major problem and this is not, I believe, what the original Halting problem was about.

So, to me, if anything, you actually put forward, like Paul Davies does in his essay, an additional limitation to computation.

So, instead of dispelling these undecidability and incompatibility problems, I think you actually add to them by considering more realistic scenarios.

Another interesting point you mention is that mathematics can only go as far as the tools of mathematics, themselves governed by the laws of physics, enable them to go.

I would venture to object that the very laws of physics we have developed are equally prone to the same critic. So I am not sure how one can be used to undermine the other.

This reminds me of Penrose's claim that the proof of Godel's first incompleteness theorem could not be checked by a Turing machine and out of which he would conclude that our brains go beyond such idealised machines. Do you have any thoughts about this?

Many thanks again for this inspiring essay.

Best of luck for the contest.

Fabien

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Hi Fabien,

Thanks for the kind words and taking the time to read my essay! I'm glad you enjoyed it and found it useful.

You raise and excellent point that I should have clearly delineated; is the halting of the algorithm equivalent to it halting because it ran out of resources? As you point and Paul point out this is a limitation on realising axiomatic systems (like mathematics) in physical hardware. I should have sharpened this point up and distinguished more clearly between the two.

Yes, I certainly believe that mathematics is limited by the laws of physics, however I understand this is a contentious point. There are many examples, which on face value appear to violate this. For example, it does not require an infinite amount of time to take the limit of an exponential decaying curve and state that it converges to zero. However, here I am not doing an infinite computation but rather using heuristics which are governed by some other computable result that doesn't require an infinite amount of time.

This ties into Penrose's point, which I currently disagree with. Our brains have a huge amount of representational power which makes them extremely fluid in moving between numerous seemingly abstract tasks. But underneath there is hardware processing this. Even our brains can't check Godel's theorems, we just have enough sense to not get caught in an infinite loop until our bodies decay. I don't believe our brains have some secret sauce that is fundamentally off-limits to a Turing machine. To leave it with a quote from Sam Harris; ``there is nothing special about a computer made of meat''.

I'm glad you enjoyed my essay. Thanks again for taking the time to read it.

Michael

Thanks for the kind words and taking the time to read my essay! I'm glad you enjoyed it and found it useful.

You raise and excellent point that I should have clearly delineated; is the halting of the algorithm equivalent to it halting because it ran out of resources? As you point and Paul point out this is a limitation on realising axiomatic systems (like mathematics) in physical hardware. I should have sharpened this point up and distinguished more clearly between the two.

Yes, I certainly believe that mathematics is limited by the laws of physics, however I understand this is a contentious point. There are many examples, which on face value appear to violate this. For example, it does not require an infinite amount of time to take the limit of an exponential decaying curve and state that it converges to zero. However, here I am not doing an infinite computation but rather using heuristics which are governed by some other computable result that doesn't require an infinite amount of time.

This ties into Penrose's point, which I currently disagree with. Our brains have a huge amount of representational power which makes them extremely fluid in moving between numerous seemingly abstract tasks. But underneath there is hardware processing this. Even our brains can't check Godel's theorems, we just have enough sense to not get caught in an infinite loop until our bodies decay. I don't believe our brains have some secret sauce that is fundamentally off-limits to a Turing machine. To leave it with a quote from Sam Harris; ``there is nothing special about a computer made of meat''.

I'm glad you enjoyed my essay. Thanks again for taking the time to read it.

Michael

Hi Michael,

I really lied this paper. Well argued. I might note also that, in the event that someone tries a Lucasesque move (à la Minds, Machines and Gödel) of claiming that the mind can see things that computers cannot, your results apply their as well. So there is no escape into the "peace and quiet" of Plato's forms: doing this would require the same kinds of dissipative processes in the brain.

Good luck - you should do well!

Best

Dean

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I really lied this paper. Well argued. I might note also that, in the event that someone tries a Lucasesque move (à la Minds, Machines and Gödel) of claiming that the mind can see things that computers cannot, your results apply their as well. So there is no escape into the "peace and quiet" of Plato's forms: doing this would require the same kinds of dissipative processes in the brain.

Good luck - you should do well!

Best

Dean

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Dear Michael James,

I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

While the discussion lasted, I wrote an article: “Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus”, due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 “Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability”.

I hope that my modest results of work will provide you with information for thought.

Warm Regards, `

Vladimir

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I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

While the discussion lasted, I wrote an article: “Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus”, due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 “Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability”.

I hope that my modest results of work will provide you with information for thought.

Warm Regards, `

Vladimir

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