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Undecidability, Uncomputability, and Unpredictability Essay Contest
December 24, 2019 - April 24, 2020
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What Is “Fundamental”
October 28, 2017 to January 22, 2018
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How can mindless mathematical laws give rise to aims and intention?
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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
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How Should Humanity Steer the Future?
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It From Bit or Bit From It
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Which of Our Basic Physical Assumptions Are Wrong?
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Is Reality Digital or Analog?
November 2010 - February 2011
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What's Ultimately Possible in Physics?
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The Nature of Time
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RECENT POSTS IN THIS TOPIC

Jonathan Dickau: on 5/18/20 at 23:40pm UTC, wrote Thank you! I look forward to your comments. Jonathan

Lawrence Crowell: on 5/18/20 at 23:13pm UTC, wrote You are playing my violin with Diophantine equations. If you read my essay,...

Torsten Asselmeyer-Maluga: on 5/18/20 at 21:19pm UTC, wrote Thanks Jonathan I also enjoyed reading you essay and gave them also the...

Jonathan Dickau: on 5/18/20 at 17:43pm UTC, wrote A wonderful essay Torsten... I had forgotten the story in 'Brave New...

Irek Defee: on 5/4/20 at 19:33pm UTC, wrote Dear Torsten, I replied to your comments about my essay in my thread. Here...

Torsten Asselmeyer-Maluga: on 4/30/20 at 13:47pm UTC, wrote Dear Cristi, thanks for your words and your time to read my essay. Your...

Cristinel Stoica: on 4/29/20 at 10:04am UTC, wrote Dear Torsten, I enjoyed very much reading your essay, in particular how...

Irek Defee: on 4/28/20 at 19:19pm UTC, wrote Dear Torsten, Thank you for your reply and promise to comment on my essay....


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FQXi FORUM
September 29, 2021

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Undecidability, Uncomputability, and Unpredictability - There is no Brave New World anymore! by Torsten Asselmeyer-Maluga [refresh]
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Author Torsten Asselmeyer-Maluga wrote on Apr. 24, 2020 @ 14:11 GMT
Essay Abstract

Here I will discuss the three important results of 20th century math and physics: undecidable theorems, uncomputable problems and unpredictable dynamics. Undecidability, Uncomputability, and Unpredictability are usually seen as a limit of knowledge. But an analysis of the three concepts paints another picture. Uncomputability is a sign of an unknown powerful bridge to other areas which are essential to solve the problem. Here, I discuss the Uncomputability of Diophantine equations and the successful solution for Fermat's equation by Wiles. Undecidability is caused by the usage of a fixed set of axioms. It disappears if we know how many steps we usually need to proof a theorem. Here, I discuss the possible Undecidability between decoherence and the wave function collapse in quantum mechanics. Unpredictability is caused by the complexity of our world. Instead to predict everything we should consider how new properties appears. Examples like evolution or explainable AI are discussed. I argue that Undecidability, Uncomputability, and Unpredictability is not a limit but a chance. The Brave New World of computable, decidable and predictable science does not exists anymore!

Author Bio

I'm a researcher at the German Aerospace Center in Berlin. My research interests vary from condensed matter physics to quantum gravity. I'm also interested in the philosophical consequences of physics. One of my main topics is the application of low-dimensional topology to cosmology.

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Irek Defee wrote on Apr. 25, 2020 @ 13:20 GMT
Dear Torsten,

There is only a couple of essays with the word Uncomputability in the title worth mentioning. Your essay is excellent and I read it with interest since it explains the concept very well. I got idea there is more to it and in my essay I take a radical vantage point with Uncomputability becoming absolutely central to everything, Theory of Everything has to be based on it. Why and how this is done is in my essay.

Best regards,

Irek

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Author Torsten Asselmeyer-Maluga replied on Apr. 28, 2020 @ 18:17 GMT
Dear Irek,

thanks for your interest and your words about my essay. I also read your essay with great interest. I understand now much better what you mean that uncomputability is central for you approach.

Ineed to say more about your essay but give with some days.

All the best

Torsten

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Irek Defee replied on Apr. 28, 2020 @ 19:19 GMT
Dear Torsten,

Thank you for your reply and promise to comment on my essay. Then I can add few words about how I see uncomputability and undecidability from the perspective of physics.

Best regards,

Irek

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Peter Jackson wrote on Apr. 28, 2020 @ 11:07 GMT
Torsten,

Great essay and analysis. I well remember your 2015 essay and you may recall our agreement. You also picked a great key phrase summarising it; "The Brave New World of computable, decidable and predictable science does not exists anymore!" You may recall my 'red/green sock trick' identifying a flawed assumption preventing classical QM.

I've suggested a key physical analogue, found in asking you to decide if a sphere is rotating clockwise or anticlockwise at any 'point' on its surface. In a random set of points some will be infinitesimally close to the equator, making it undecidable! Then the same with linear motion nearing the poles.

I don't recall if you read mine last year but it shows how the QM data can be reproduced by simple exchange of momentum in measurement.I touch on it this year, but approach it in a more fundamental way also suggesting a way to correct the paradoxes in philosophy, logic and maths. I hope you'll look and comment for me.

All is consistent with your excellent contribution, which I see has a ridiculously low score, probably trolled with 1 scores as mine has been! My top score will somewhat correct that!

Well done and very best of luck in the contest.

Peter

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Author Torsten Asselmeyer-Maluga replied on Apr. 28, 2020 @ 18:22 GMT
Dear Peter,

thanks for your interest and in particular for your vote (you are right: someone voted 5 minutes after appearing)

I hope to find time to read your essay and comment on it soon. I'm sure rhat I will like it.

very best luck in the contest too

and more later

Torsten

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Cristinel Stoica wrote on Apr. 29, 2020 @ 10:04 GMT
Dear Torsten,

I enjoyed very much reading your essay, in particular how you introduced and explained the concepts, and how you conducted the arguments. But most importantly, I liked the positive twists that you put on things that we normally take as limitations from the important no-go theorems that we have.

> Undecidability, Uncomputability, and Unpredictability are usually seen as a limit of knowledge. But an analysis of the three concepts paints another picture. Uncomputability is a sign of an unknown powerful bridge to other areas which are essential to solve the problem.

I fully agree with this, understanding the walls helps understanding and finding the doors. You gave some great examples, showing that indeed, as you wrote, "The Brave New World of computable, decidable and predictable science does not exists anymore!" Braver freer worlds are waiting for us beyond this one. Probably researchers will never run out of wonderful problems to explore. Even though the difficulty will grow like Gödel's φ(n), the power of our tools will hopefully grow too. All this time, epistemological modesty grounded in the no-go theorems will be our faithful friend.

Thanks for this essay, and success!

Cheers,

Cristi

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Author Torsten Asselmeyer-Maluga replied on Apr. 30, 2020 @ 13:47 GMT
Dear Cristi,

thanks for your words and your time to read my essay. Your essay is also on my reading list.

Yes, I like much more to write an overview then the discussions of special aspects (I saw it very often in the contest).

I try to write you soon about your essay.

Good luck in the contest

Torsten

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Irek Defee replied on May. 4, 2020 @ 19:33 GMT
Dear Torsten,

I replied to your comments about my essay in my thread. Here are some thoughts about your essay. I think the undecidability and uncomputability as they are usually considered have nothing to deal with physics. This sounds provocative but the reason I see it like this is if we take e.g. this paper about undecidability of spectral gap. So the gap is undecidable but it is decided...

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Jonathan J. Dickau wrote on May. 18, 2020 @ 17:43 GMT
A wonderful essay Torsten...

I had forgotten the story in 'Brave New World' and did not immediately make the connection that you were talking about the people in the book being boxed in by certainty, where this possibility is now excluded. But I like very much that you concluded that the 3 'uns' leave things more open-ended or encouraging. It was a pleasure to read a paper that includes plenty of math inline without it getting cumbersome or forcing the reader to do a difficult evaluation without connection back to the text. Your Maths read like part of the story instead. I like that.

It was especially cool that you were able to offer several historical examples where what appeared to be a roadblock in Maths turned out to be a pivot point instead, or forced progress to move in a new direction, so it was helpful rather than a hindrance. That was both gratifying and educational to read.

And finally; I am glad you were able to work in some discussion of the merits for decoherence and collapse models in QM. I had some enjoyable correspondence with Dieter Zeh, prior to his demise, and he always seemed eager to show that decoherence is fundamentally different from wavfunction collapse. Years before; I had some contact with Phil Pearle, when he was first developing the Statevector Reduction model, because he was one of my sister's professors. I still have a typewritten preprint of the 'gambler's ruin' paper somewhere.

I am forced to give you very high marks for this short but quite excellent essay. I think you might enjoy mine.

All the Best,

Jonathan

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Author Torsten Asselmeyer-Maluga replied on May. 18, 2020 @ 21:19 GMT
Thanks Jonathan

I also enjoyed reading you essay and gave them also the maximum score.

Unfortunately I'm to late this year (because of COVID19).

I have to comment about your ideas in your thread.

All the best

Torsten

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Jonathan J. Dickau replied on May. 18, 2020 @ 23:40 GMT
Thank you!

I look forward to your comments.

Jonathan

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Lawrence B. Crowell wrote on May. 18, 2020 @ 23:13 GMT
You are playing my violin with Diophantine equations. If you read my essay, which maybe you have, I employ that as a way of looking at obstructions between entanglement types transforming into each other by unitary means. The comment about the quantic and elliptic functions is close as well.

If you read Palmer's essay you find there is a fractal-like logic and p-adic numbers. The "ultimate" fractal in some ways is the Mandelbrot set that has branching patterns that are Fibonacci. I think entanglement symmetries have Bott periodicity, where very large N entanglements have symmetry equivalent to that of N mod8. Then this fractal nature then gives the set of entanglements relevant are 2, 3, 5 and 8 --> 0 entanglements, the bipartite, tripartite, quinpartite and so forth. The 8-fold is a sort of bipartite entanglement of 2 4-tangles. The 5-tangle is "weird," and this I have speculated has connections with the quintic.

U don't have time now, but I understand a lot about the role of the exotic M^4 and I think it plays a role on black holes.

Cheers LC

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