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Undecidability, Uncomputability, and Unpredictability Essay Contest
December 24, 2019 - April 24, 2020
Contest Partners: Fetzer Franklin Fund, and The Peter and Patricia Gruber Foundation
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What Is “Fundamental”
October 28, 2017 to January 22, 2018
Sponsored by the Fetzer Franklin Fund and The Peter & Patricia Gruber Foundation
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Wandering Towards a Goal
How can mindless mathematical laws give rise to aims and intention?
December 2, 2016 to March 3, 2017
Contest Partner: The Peter and Patricia Gruber Fund.
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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation
Media Partner: Scientific American

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How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American
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It From Bit or Bit From It
March 25 - June 28, 2013
Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American
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Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American
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Is Reality Digital or Analog?
November 2010 - February 2011
Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American
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What's Ultimately Possible in Physics?
May - October 2009
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The Nature of Time
August - December 2008
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Neil Bates: on 5/19/20 at 0:03am UTC, wrote Dear Mr. Vastola, This is a very deep and well-written essay on...

John Vastola: on 5/18/20 at 22:09pm UTC, wrote Thank you for reading, and for your very kind words! I agree that these...

John Vastola: on 5/18/20 at 22:07pm UTC, wrote Thanks for reading! Assuming Laplace's demon is part of the universe, it is...

John Vastola: on 5/18/20 at 22:01pm UTC, wrote Thanks for reading, and for the compliments. Interesting point, I'll have...

John Vastola: on 5/18/20 at 21:58pm UTC, wrote Thank you for reading, and thank you for your very thoughtful comments....

Cristinel Stoica: on 5/18/20 at 17:54pm UTC, wrote Dear John, I enjoyed your essay, which combines in a spectacular way...

Yutaka Shikano: on 5/17/20 at 22:51pm UTC, wrote Dear John, Your essay has a lot of contents to be tied by the concept of...

Jochen Szangolies: on 5/16/20 at 9:38am UTC, wrote Dear John, you present an intriguing approach, and choose an original way...


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FQXi FORUM
October 20, 2020

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Can Brazilian butterfly flaps destroy the universe? How fundamental limits on knowledge and computation force Laplace's demon to become a scientist by John Joseph Vastola [refresh]
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Author John Joseph Vastola wrote on Apr. 24, 2020 @ 00:30 GMT
Essay Abstract

What questions can ever be answered by a physical entity? In this essay, we examine this question by studying the predictive powers of Laplace's demon. We find that the powers of a physical Laplace's demon are considerably diminished by limits on what is knowable due to quantum mechanics, (classical and quantum) chaos, incompleteness, and physical limits on computation. Because the helplessness of Laplace's demon naively conflicts with the shocking comprehensibility of the world around us, we imagine a new demon intended to model what questions can ever be answered. The approach and capabilities of this demon are found to strongly resemble those of scientists. We touch on some consequences of our arguments, including for free will and predicting versus understanding.

Author Bio

John Vastola is a fourth year Ph.D. student in the Department of Physics and Astronomy at Vanderbilt University.

Download Essay PDF File

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Michael James Kewming wrote on Apr. 24, 2020 @ 03:31 GMT
Hi John,

Great essay, I really enjoyed it!

I'm curious whether you are treating the idea of Laplace's demon as an equivalent to a Universal Turing machine? The five tools you equipped the demon with are very similar to the indelible tools of a Turing machine i.e read, write, process and memory. As you point out, the unanswerable questions of the demon are also undecidable problems of a Turing machine.

Michael

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Author John Joseph Vastola replied on May. 2, 2020 @ 03:15 GMT
Thanks for reading!

That's a good question. Since, at the end of the day, Laplace's demon is essentially just a really high-end computer, you're probably on to something. I never thought about the parallels between reading/writing/processing memory and thinking/doing experiments, but they seem pretty striking now that you point them out.

If there is any difference between them, it is probably only the moral difference that I'm emphasizing the demon's ability to 'think' in terms of different (possibly emergent) vocabularies. It calls to mind our own ability to do such a thing: how can we so adeptly switch between thinking about a shirt, its fabric, and the atoms that make it up? There must be a way to compute when it's appropriate to use one vocabulary or another, but it seems hopelessly difficult to pin down what that algorithm might look like in general.

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Satyavarapu Naga Parameswara Gupta wrote on Apr. 24, 2020 @ 05:19 GMT
Dear John Joseph Vastola,

Wonderful essay on Laplace's demon!!

I will make three or four posts on your nicely argued essay on different subjects. Each discussion will have its own thread, Ok?

I worked and developed on Dynamic Universe Model for the last 40 years under Maa Vak's guidance, which is an N-Body problem solution, Mathematically stable,and many of its predictions came true. See my paper / essay here for further details...

"A properly deciding, Computing and Predicting new theory’s Philosophy"

I did a lot of theoretical and practical experimentation on this model which gave positive results.

With this introduction I will go for analyzing and discussing in the next posts

Best wishes

=snp

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Author John Joseph Vastola replied on May. 2, 2020 @ 03:16 GMT
Thank you for the thoughtful comments! I'll definitely take a look at your essay.

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Satyavarapu Naga Parameswara Gupta wrote on Apr. 24, 2020 @ 05:33 GMT
Dear John Joseph Vastola,

Subject: Flipping the wings of Black witch moth evaporates whole universe into vacuum!

How such thing happens, then what happens to the all the matter in Universe, will change into energy by exploding into a Bomb???

On what conditions it may happen for example like a Bigbang!!

Thought provoking essay

Best Wishes

=snp

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Satyavarapu Naga Parameswara Gupta wrote on Apr. 24, 2020 @ 06:26 GMT
Dear JJ Vastola,

Subject: Laplace's demon, the hypothetical vast intelligence

Your words:

......................First described by the eminent scholar Pierre-Simon Laplace in an 1814 essay. If the universe really did consist of nothing but a large number of particles obeying Newton's laws of motion, Laplace reasoned, then an intellect that (i) knew the positions and momenta of all particles at one time and (ii) could accurately solve Newton's equations of motion given that data, could know any future or past state of the universe with absolute certainty.............

Main problem comes in Newtonian Physics or Einstein type Relativity based Physics is , they assume a single body and develop gravitation field around it in their own way. Multiple bodies of different sizes and different three dimensional positions are not taken.

But in Dynamic Universe Model, a similar concept was taken, or in other words as what you mentioned in your essay posted as above, was taken about 40 years back. 132 bodies were taken, with some realistic positions and masses on a computer and tried to solve for exact positions and trajectories under mutual gravitation.

Why 132 bodies you may ask. Then at that time i could afford to buy a Computer two floppy drives. In one I used to load lotus 123, and the second drive is filled with data .

The same Model software "SITA" developed at that time worked well excellently. Solved all the problems, Ofcource, Now "SITA" is transported to "Excel"....

Have a look at Blog...

' http://vaksdynamicuniversemodel.blogspot.com/p/blog-page_15.
html '

Please tell few words about this.....

Best

=snp

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Author John Joseph Vastola replied on May. 2, 2020 @ 03:21 GMT
Judging the correctness of your theory is beyond my pay grade, I'm afraid. It looks very interesting, though.

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Satyavarapu Naga Parameswara Gupta wrote on Apr. 24, 2020 @ 07:34 GMT
Dear JJ V,

I am continuing with another post.... Your words for reference.....Suppose for the moment that Newtonian physics offers the correct description of the universe, and that Laplace's demon knows the current positions and momenta of all particles in the universe to only Finite precision...............

Now coming to "Dynamic Universe Model"

I took all this work to be in Cosmology only, did not go into Quantum Physics; was under guidance by Maa Vak, took masses from NASA, Positions from Astronomical Ephemeris as on 01,01;2000 at 00.00 hrs as a starting basis for calculations....

Dynamic Universe model calculates UGF the Universal gravitation force acting on a perticular body by all the bodies in the Universe at that instant of time for that positional setup. This UGF is not a constant, but varies with time and position, as all the bodies are moving DYNAMICALLY all the time.

I hope this is clear....

Best

=snp

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Satyavarapu Naga Parameswara Gupta replied on Apr. 24, 2020 @ 08:05 GMT
Dear JJV,

I forgot to add the precision in calculations is " 10-16 %" parts accuracy as available in Excel.

Precision in measurement is may be " 1% " as the data available....

Your comments please

Best

=snp

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Satyavarapu Naga Parameswara Gupta wrote on Apr. 24, 2020 @ 08:14 GMT
Dear JJV,

Your words.............. Laplace's demon knows the current positions and momenta of all particles in the universe to only finite precision instead of infinite precision; in other words, suppose that there is a small amount of error in its knowledge of the current state of the universe.

How much does this initial inaccuracy affect its ability to predict the future, or retrodict the past? It turns out that most deterministic dynamical systems|like collections of interacting particles obeying Newton's laws|exhibit chaos, ...............

NO CHAOs ANY TIME You verify published books and papers of Dynamic Universe Model........... !!

Best

=snp

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Satyavarapu Naga Parameswara Gupta wrote on Apr. 24, 2020 @ 08:16 GMT
Dear JJV,

I will stop for now, by seeing your response, I will discuss some more..........

Best

=snp

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Martin Perry wrote on Apr. 24, 2020 @ 18:49 GMT
I really appreciated this analysis and taking to task of Laplaces' demon. As someone unfamiliar with a lot of these examples I found myself still gripped and interested by the elegant and matter of fact writing style you had. It really made the subject much more tenable to grasp for all kinds of readers, something not easily done by many in your field. All in all an eloquent paper that satiated my curiosity while at the same time piqued my interest for more understanding of the other topics and examples you brought up.

-M. Perry

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Author John Joseph Vastola replied on May. 2, 2020 @ 03:28 GMT
Glad you liked it! Thank you for reading.

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James Lee Hoover wrote on Apr. 25, 2020 @ 18:23 GMT
John,

Quite a bit to unpack, John, but quite accessible and interesting. With somewhat of a liberal arts background, I appreciate the imagery of the black witch moth and the legendary specter of death it depicts. Chaos theory for this subject is appropriate as well. Like the way you characterize the problem the contest assigns. I like it that you don't pretend to know the answers but impose on us many relevant truths. One point suggested is that our cognitive powers have evolved to suit our environment, something I believe I touch upon, and our classical level perceptions have necessarily not incorporated quantum truths, which I also touch upon. My rating is your fourth, which I mention because we have an evaluator who gives 1s w/o comments sometimes choosing to time it with those who comment. I rate it among the highest.

Jim Hoover

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James Lee Hoover replied on Apr. 25, 2020 @ 18:28 GMT
John,

LOoks like I'll have to wait to rate.

Jim

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Author John Joseph Vastola replied on May. 2, 2020 @ 03:27 GMT
Thank you for the kind words, Jim. Yes, I found the imagery of the black witch moth (and some of the surrounding folklore) quite captivating as well.

The point about our cognitive powers evolving to suit our environment is important, I think. I'm not sure what it would be like to wield a different set of cognitive powers, but I'm sure some kind of different brain architecture (or maybe even no centralized brain at all, a la jellyfish) is physically conceivable. And if it was appreciably different, maybe our ability to understand the world would be appreciably different too.

I'll definitely take a look at your essay!

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James Lee Hoover replied on May. 2, 2020 @ 17:02 GMT
John,

It's always good to see that someone reads your essay with some interest and with keen comments. I thinks it helps to promote the kind of analysis and thinking the foundation means to foster. Thanks, for reading and for your incisive remarks. I didn't get a chance to rate yours before, but I will now. It will be your 6th since people bomb at the time of comments.

Jim

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Shiwani Varal wrote on Apr. 26, 2020 @ 09:15 GMT
Dear JJ Vastola,

I really enjoyed reading your discussion and analysis of Laplace's Demon and quantum mechanics. You have a very creative style of exemplifying complex ideas into simple notions without losing the true essence of the concepts. Your essay raised many ideas in my head about the attempt of different mathematicians who attempt to come up with a single equation that describes the underpinnings of this universe, and in some sense, it made me think more about the P vs. NP problem as well. I know I am connecting all these things, but I am genuinely intrigued by the honesty reflected in your essay. Thank you for sharing your work.

Best,

SV

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Author John Joseph Vastola replied on May. 2, 2020 @ 03:30 GMT
Thank you for reading! Yes, it's fascinating to wonder about the possibility that we can describe the universe in complete detail via some equation or set of equations. What might that equation look like? Could we comprehend it? We can comprehend things like the Schrodinger equation quite well, but it remains to be seen whether it or something like it offers the full story.

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Flavio Del Santo wrote on May. 3, 2020 @ 17:30 GMT
Dear John,

thank you for a very well-argued and interesting essay. No doubt one of the best I have read so far (and I have read quite some by now!). I also see a great deal of common elements between our views.

Your variant of demon that aims at operationalizing Laplace's demon is really insightful. I see in your essay the seeds of something that I have been thinking for quite awhile...

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Author John Joseph Vastola replied on May. 7, 2020 @ 18:19 GMT
Thank you for the very kind words, Flavio!

I agree that information being "inaccessible in principle" is a useful concept, and that one must be mindful that determinism vs indeterminism may not be black and white. However the universe really 'is', there are ample restrictions on what we can know about it...whether it's better to describe the universe as it 'is' or in terms of what we can ever possibly know about it is an interesting question. I don't pretend to know the answer!

Great point about classical vs quantum mechanics. I really enjoyed discussion along these lines in your essay, and never thought before about the strong metaphysical assumption that observables really 'are' determined to infinite precision in classical mechanics, though our ability to measure them is restricted. Perhaps they are not determined to infinite precision. It's hard to imagine a way to tell the difference. Still, which formulation is more useful in practice is amenable to debate/discussion, I think.

Thanks for the paper link, I'll take a look at it.

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David Jewson wrote on May. 4, 2020 @ 08:14 GMT
Dear John,

Wow! What an essay.

I would like to imagine a world where Laplace’s demon could answer all questions about the future in that world. So, say the world worked like a fractal. It was generated by a simple algorithm, so it started with a single number in space and then rapidly expanded with ever more numbers added, becoming ever more complex. Say it not only generated new numbers in space but also changed the already created numbers. There would then be space full of change, a little like our own world.

If someone asked a question about how the fractal would look in the future, the demon could then answer it by restarting the algorithm in another place and just running it at a much faster speed than the original. It would need to be assumed that the demon, its model, and the person asking the question would all need to be outside the original fractal. Also, that there was constant creation in that world, so no unitarity!

I only mention this, as I think there is an interesting argument to say that Quantum Mechanics could be reinterpreted as a simple algorithm expanding the Universe in a fractal like way (see my essay if you are interested).

Thanks for a beautifully written, clear and thought-provoking essay, with a very well-argued conclusion.

All the very best,

David

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Author John Joseph Vastola replied on May. 12, 2020 @ 14:04 GMT
Thank you for reading, and for the kind comments! That's an interesting idea. What do you mean by saying that the demon/its model/the person should be outside the original fractal? To me, it's important to imagine that all of them are a part of the universe, as we are. Given your idea about a fractal-like universe, what can a demon inside the fractal know?

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David Jewson replied on May. 16, 2020 @ 09:32 GMT
In the fractal world I suggested, that is a world constructed from scratch using a basic algorithm, if you looked at the world from outside, you would see people and other things in it. They might appear to have free will, but all their actions would be determined by the algorithm. We might see the demon within the same world, and we might see that he’s appeared to discover the algorithm and has started running his own algorithms – but again all his actions would be the result of the original algorithm, which would be giving an illusion of free will and purpose. The demon might be seen, in his part of the fractal, building a world from scratch using the same rules as the fractal does, but, because his actions and their speed are actually all actions of the basic algorithm, he can’t outpace it and, therefore, can’t do the predicting.

There’s another problem for the demon: if he wants to build a complete model of the world, it has to include his model, which also needs to include that model and so on. It’s like building a model village inside the village itself. The model has to contain a model, which has to contain a model and so on indefinitely. The model then has to have infinite parts which is impossible.

So, as part of the fractal he can’t have complete knowledge. However, if somehow, with his demon like nature, he wasn’t part of the original fractal, i.e., he wasn’t under control of the basic algorithm, he could then build his own fractal, and if it was identical to the original but just ran faster, he could predict exactly everything that the original would do in the future.

Thanks again for a lovely essay.

P.S. Thanks also for taking the time and effort to read my essay. What you said really made me think. I’ve posted a reply which I hope you will also find interesting.

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Luca Valeri wrote on May. 8, 2020 @ 20:32 GMT
Dear John,

I enjoyed a lot to read your essay. Laplace demon is hunting since a long time. I hoped your essay could help me, to get rid of him. One good thing is, that you made him physical and took him a few of his superpowers. But by submitting him to the epistemic restriction we as human have, or any physical object, that can transmit or gather information, does not chase away the metaphysical demon. In fact, how you describe the relation between, what can known and what is, is in the traditional realist fashion.

To chase a way the metaphysical demon, one has to justify, why epistemic notions should matter at all for the understanding of our universe.

I like how you equip your physical demon. Von Weizsäcker, who wanted to construct a time dependent formal logic, took an operational approach to formal languages and mathematics. While animals instinctively react (take action) on sensory inputs, humans can imagine the actions they take. He constructs the meaning of propositions as imagination of possible actions. This - I think - is what is described in your points 1 to 4 for the equipment for the demon.

Von Weizsäcker's approach does, in my opinion, bridge the somehow artificial gap between the meaning of concepts of a formal language and the 'concepts of the physical world'. This because the formal concepts depend on the laws themselves. I belief this could chase out the metaphysical demon.

How such a world without this demon could look like is described in my essay.

Luca

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Author John Joseph Vastola replied on May. 12, 2020 @ 15:36 GMT
Thanks for reading! Interesting, I've never heard of Von Weizsäcker (I don't know much about philosophy, to be honest). I like your essay, but I am still a bit confused about how we can know whether a given theory is semantically closed.

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Lachlan Cresswell wrote on May. 10, 2020 @ 14:35 GMT
Dear John,

I enjoyed your very readable demon essay.

I liked the way you first introduce the demon as LaPlace did as an omnipotent being, the considered the consequences of the demon inside the Universe and then eventually 'humanised' the demon and consider what we can eventually learn given more time and analysis of future experiments.

I also discuss the demon in my essay, albeit in a much briefer fashion, and draw some conclusions as well, before invoking Maxwell's demon as well. I hope you enjoy my angles, as much as I enjoyed yours!

Best Regards,

Lockie Cresswell

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Author John Joseph Vastola replied on May. 12, 2020 @ 15:07 GMT
Thanks for reading! Yes, your essay was very interesting.

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Alyssa Adams wrote on May. 11, 2020 @ 00:43 GMT
Hi John!

This was a very nice essay! I really enjoyed thinking about several aspects of Lapace's Demon, and the modified demon you talk about here. I think you're exactly on-point, even if all of our current math and physics can be programmed into such an entity, there are still tons of things that are unknowable.

I wonder, have you thought about the limit of the size of Laplace's Demon to where it is the size of the entire universe? What is the universe itself is Laplace's Demon? Personally, I think this limit would imply the universe does indeed "know" everything about itself, and is likely a boring trivial result. But, then working backward from size, what is the demon was the universe minus one atom? How would it change things?

Cheers!

Alyssa

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Author John Joseph Vastola replied on May. 12, 2020 @ 13:28 GMT
Thanks for reading! Great question. My inclination is to believe that it would take a computer as big as the universe to effectively simulate the universe in complete detail---as you said, the universe should 'know' everything about itself! But I don't know how much power a universe-sized demon would lose for each atom you take away. You could say it loses a 'small' amount, but how do you define small here? What's the critical number of atoms or particles you have to take away in order for it to be effectively incapacitated (like a demonic ship of Theseus)? Hard to say.

Although I didn't specify in the essay, I think in any case that it's more interesting to speculate about a demon whose size is small compared to the universe overall. Partly because it's hard to imagine such a demon doing experiments, thinking (is its ability to think hampered somehow by the finite speed of light?), and communicating with us. And partly because I was thinking about the demon as an idealization of our own struggle to understand the universe.

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James Lee Hoover wrote on May. 12, 2020 @ 06:12 GMT
John,

Hope you have time to check mine out before the deadline: https://fqxi.org/community/forum/topic/3396

Jim Hoover.

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Author John Joseph Vastola replied on May. 12, 2020 @ 13:19 GMT
Jim, I commented on and rated yours on May 2nd.

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Pavel Vadimovich Poluian wrote on May. 15, 2020 @ 07:06 GMT
Dear John J. Vastola!

Thank you for the beautiful and informative article. We hope you will be happy with our message. We put up 10 points for your essay. You described the problem both scientifically and poetically, but we want to note an important circumstance. We believe that a crazy demon may not help us in the world game. But there is a difference between the fundamental laws (rules of the game) and the laws governing this chess game. The latter are clearly algorithmic, which means they are volatile.

We wish you successful research!

Truly yours,

Pavel Poluian and Dmitry Lichargin,

Siberian Federal University.

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Author John Joseph Vastola replied on May. 18, 2020 @ 22:01 GMT
Thanks for reading, and for the compliments. Interesting point, I'll have to read your essay to learn more.

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Jochen Szangolies wrote on May. 16, 2020 @ 09:38 GMT
Dear John,

you present an intriguing approach, and choose an original way to attack the omniscience of Laplacian demons---I have not previously come across the Reeh-Schlieder theorem used in this way. To me, your discussion of what can be known, what answers can be obtained suggests an approach to doing science that's in a sense top-down: you formulate constraints regarding knowability, and...

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Author John Joseph Vastola replied on May. 18, 2020 @ 21:58 GMT
Thank you for reading, and thank you for your very thoughtful comments. It's been a great pleasure, as part of this essay contest, to throw out some ideas and see people really engage with them (and vice versa).

I'm very sympathetic to your point about my 'we focus on understanding the understandable/easy problems' comment. I think that, although many non-scientists may disagree, it's...

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Yutaka Shikano wrote on May. 17, 2020 @ 22:51 GMT
Dear John,

Your essay has a lot of contents to be tied by the concept of Laplace's demon. I have two fundamental questions on your essay.

Under the assumption that Laplace's demon is itself part of the universe, what physics laws is Laplace's demon subject to?

In physics, our theory is experimentally verifiable. This seems to be the fundamental concept of laws of physics. Then, how to verify your assumptions on Laplace's demon?

Best wishes,

Yutaka

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Author John Joseph Vastola replied on May. 18, 2020 @ 22:07 GMT
Thanks for reading! Assuming Laplace's demon is part of the universe, it is subject to all the same physical laws we are, e.g. it cannot communicate information faster than the speed of light, it can only measure observables (and not things like wave function values), it has finite memory and computational speed, and so on.

Of course, there is no way to verify my assumptions regarding Laplace's demon, because Laplace's demon is not real; it's just a helpful device for thinking about what is (in principle) possible. But on the other hand, I think it's hard to reasonably argue that a being part of the universe could violate some of the restrictions I mentioned (e.g. communicating faster than light speed, measuring things that aren't observable, having infinite memory and computational speed). Laplace's demon isn't a theory so much as a tool that helps us think about the consequences of our existing theories.

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Cristinel Stoica wrote on May. 18, 2020 @ 17:54 GMT
Dear John,

I enjoyed your essay, which combines in a spectacular way science with poetry and philosophy. I liked how you connected the nonlinear dynamics with quantum mechanics. I particularly liked the discussion of the Reeh-Schlieder theorem. You remarked very well how a quantum Laplace daemon would fail to verify what predicts, but also how he (and us, of course), can do the next best thing. Things are not that dark with these limitations, especially if you see the bright side, which is that of allowing us freedom and an open future. I wish you success in the contest!

Cheers,

Cristi

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Author John Joseph Vastola replied on May. 18, 2020 @ 22:09 GMT
Thank you for reading, and for your very kind words! I agree that these limitations are not cause for pessimism---it's amazing that we can understand so much about the universe, given all these obstacles in our way. The next best thing to knowing everything really isn't so bad.

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Neil Bates wrote on May. 19, 2020 @ 00:03 GMT
Dear Mr. Vastola,

This is a very deep and well-written essay on connections between thermodynamics and quantum mechanics. I admire that it does not just rehash familiar tropes about quantum measurement, interference and the like. One issue I noted when reading on the subject: curiously, the principles of optics "conspire" to prevent violation of the Second Law, by preventing a system from focusing to a surface brightness more than the source (IOW, through a minimum allowed f/ratio. Otherwise, image brightness could be increased without limit. I leave the consequences "as an exercise for the reader."

You and others might find my essay interesting, and it could use more votes on this last day. I discuss the limitations on realistic models of "superluminal signalling" to explain the correlations of entanglement. Pardon inactive link.

https://fqxi.org/community/forum/topic/3548

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