Undecidability, Uncomputability, and Unpredictability - There is no Brave New World anymore! by Torsten Asselmeyer-Maluga

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

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

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

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 by physical matter all the time. One thus ask how is that possible but after a moment of reflection this is trivial: undecidability deals with a model of computation but matter is not computing according to this model. Matter conforms to the requirements of symmetry and these have form reflected by mathematics which is about symmetries. But nothing is computed in the sense of computers.

Uncomputability is similar since its stuff is infinite and that is questionable for physics. Idea of essay is based on uncomputable sequences from which math and physics emerge, and thus physics can be finite but running on uncomputable substrate.

Unpredictability is another issue and a very important question is where is the source at the most fundamental level, maybe it is in the incompletness of arithmetic and thus math?

By the way, you mention brain and consciousness in your essay. I think these items are much worse than physics, quantum field theory and quantum gravity:) in the sense that absolutely nothing can be said about anything there with any degree of certainty. One can take single neurons as example, they are modelled as threshold elements but real neurons are by far not like this. All the time there are coming new data showing they are extremely complicated, dendrites and axons are not only simple wires, synapses are not simple switches, cellular scaffolding aorund neurons is not passive and so and so on. So we do not even know what is really single neuron doing, assemblies of neurons are much more complicated. I've been in the area of image processing and pattern recognition and things there are really ad hoc.

Br,

Irek

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

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