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FQXi FORUM
August 12, 2020

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Undecidability and unpredictability: not limitations, but triumphs of science by Markus P Mueller [refresh]
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Author Markus P Mueller wrote on Apr. 21, 2020 @ 11:12 GMT
Essay Abstract

It is a widespread belief that results like Goedel’s incompleteness theorems or the intrinsic randomness of quantum mechanics represent fundamental limitations to humanity’s strive for scientific knowledge. As the argument goes, there are truths that we can never uncover with our scientific methods, hence we should be humble and acknowledge a reality beyond our scientific grasp. Here, I argue that this view is wrong. It originates in a naive form of metaphysics that sees the physical and Platonic worlds as a collection of things with definite properties such that all answers to all possible questions exist ontologically somehow, but are epistemically inaccessible. This view is not only a priori philosophically questionable, but also at odds with modern physics. Hence, I argue to replace this perspective by a worldview in which a structural notion of ‘real patterns’, not ‘things’ are regarded as fundamental. Instead of a limitation of what we can know, undecidability and unpredictability then become mere statements of undifferentiation of structure. This gives us a notion of realism that is better informed by modern physics, and an optimistic outlook on what we can achieve: we can know what there is to know, despite the apparent barriers of undecidability results.

Author Bio

Markus P. Mueller obtained his PhD in 2007 at the Technical University of Berlin. After a postdoctoral position at the Perimeter Institute for Theoretical Physics (where he is still a Visiting Felllow), he has been a Junior Research Group Leader at Heidelberg University, Germany. From 2015-2017, he has been an Assistant Professor at the Departments of Applied Mathematics and Philosophy at the University of Western Ontario, where he was holding a Canada Research Chair in the Foundations of Physics. Since 2017, he has been a Group Leader at the Institute for Quantum Optics and Quantum Information (IQOQI) in Vienna.

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Jochen Szangolies wrote on Apr. 21, 2020 @ 14:26 GMT
Dear Markus,

I'm happy to see you've found the time to enter an essay into this year's competition. Like last year's, it's a highly intriguing and insightful piece, and I'll spend some quality time studying it further. I like the way you frame the discussion: undecidability and related phenomena need not fuel defeatist stances, you enlist them in an optimist message about our ability of...

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Author Markus P Mueller replied on Apr. 22, 2020 @ 06:33 GMT
Dear Jochen,

thank you so much for taking the time to read my essay -- and, in particular, for the excellent comments!

I'm glad that you've pointed me to Karl Svozil's piece. I wasn't aware of it, and I've put it on my reading list.

For now, let me comment only on Newman's objection. I'm not an expert on all of the nuanced ways that it is interpreted in detail, and on the...

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Jochen Szangolies replied on Apr. 22, 2020 @ 10:44 GMT
Dear Markus,

thanks for your reply. I think you're right regarding OSR and the Newman Objection, at least as it's usually conceived. I'm not totally convinced by the argument, though. To me, there seems to be a threat of a priori considered to be distinct structures collapsing onto one another---any claim to theory A giving the 'right structure' can be challenged by some theory B yielding...

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Jochen Szangolies replied on Apr. 23, 2020 @ 05:33 GMT
Dear Markus,

I've finally gotten round to giving your essay the reading it deserves. I think it's in some ways very close to my own thinking, and a few years back, I would've heartily endorsed all of its claims---indeed, in my entry to the 'It from Bit'-FOXi contest, I expressed similar reservations against 'thingism': "The world is then not something comprised, at the very bottom, of...

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David Brown wrote on Apr. 21, 2020 @ 14:46 GMT
"... there is a widespread view of quantum physics which regards its statistical character as a symptom of incompleteness ..." Is "quantum physics" a well-defined concept? Is "spacetime" a well-defined concept? Is a “potential infinity” a well-defined concept? Consider the following hypothesis: For every positive integer n, if nature contains n bits of information then nature contains n+1 bits of information. I suggest that there is empirical evidence that the preceding hypothesis is false. Why do I suggest this? I say that dark-matter-compensation-constant = (3.9±.5) ^ 10^–5 ... contrary to the widespread belief that dark-matter-compensation-constant = 0. If dark-matter-compensation-constant were equal to 0, it seems to me unlikely that Wolfram's cosmological automaton would work. I conjecture that the 4 ultra-precise gyroscopes of Gravity Probe B worked correctly. Why do the string theorists think that Milgrom's MOND is wrong? First, they refuse to carefully study the empirical evidence. Second, they realize that string theory with the infinite nature hypothesis makes any string theoretical explanation of MOND extraordinarily complicated and rather dubious in terms of their paradigm.

What might be wrong with Kroupa’s analysis?

Kroupa, Pavel. "The dark matter crisis: falsification of the current standard model of cosmology." Publications of the Astronomical Society of Australia 29, no. 4 (2012): 395-433.

arXiv preprint

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Joe William Fisher wrote on Apr. 21, 2020 @ 15:38 GMT
Dear Professor Mueller,

After I had notified over three-hundred visible credentialed physicists that Nature must have provided the only VISIBLE physical structure allowable and that there had only ever been ONE VISIBLE infinite contrasting surface eternally occurring in ONE infinite dimension while always mostly being illuminated by ONE infinite form of finite non-surface light, you were the only visible person to respond. You agreed with me that all visible physicists and philosophers (including Rene Descartes) had always guessed about the structure of the universe, and you modestly admitted that you had only ever made “good” guesses, not arbitrary guesses. You certainly seem to have filled your essay with lots of guesses.

Joe Fisher, Visible Realist

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H.H.J. Luediger wrote on Apr. 21, 2020 @ 20:43 GMT
Dear Markus Müller,

interesting essay, but too post-modern for my taste: never call a problem a problem, at most a challenge or ideally, make it into the solution.

Heinz

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Author Markus P Mueller replied on Apr. 22, 2020 @ 06:39 GMT
Dear Heinz,

thanks for your feedback!

I'm *not* denying that there are severe problems in the world that can't simply be argued away. Of course there are many (climate change for example), and we should acknowledge these problems and work hard on a solution.

All I'm saying in my essay is that unpredictability and undecidability are not among those.

Best,

Markus

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Charles John Sven wrote on Apr. 22, 2020 @ 20:28 GMT
Dear Professor Mueller :

I like your views on the question of Undecidability, Uncomputability, and Unpredictability:

Our only limitation is data; if we have the data then the proof is possible. If the data is not available then the proof is uncomputable. The undecidability question becomes whether or not we have all the data. Finally, unless we are clairvoyant we have no observational data about the future, consequently any prediction made is a projection of history and subject to falsification.

Just giving a name to something is not data. Richard Feynman: The Difference Between Knowing the Name of Something and Knowing Something.

A nonanswer may be proof that the data does not exist or one does not have all the data or that the data is unrecognized.



It is proposed that any evidence describing the Big Bang is beyond science’s reach and yet this essay [entered January 18th below] “Common 3D Physics Depicts Universe Emerging From Chaos” presents a plausible description with plenty of replicable evidence.

Respectfully,

Charles Sven

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Author Markus P Mueller replied on Apr. 23, 2020 @ 12:21 GMT
Dear Charles Sven,

thank you for your kind words.

I also like Feynman's tale about the bird a lot. It reminds us not to conflate people's opinions or ideas with the actual matters of fact.

I'll have a look at your essay.

Best,

Markus

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Flavio Del Santo wrote on Apr. 23, 2020 @ 00:05 GMT
Dear Markus,

thank you for this well-argued essay, which I enjoyed very much. You managed to give a new perspective to a notorious analogy between incompleteness in maths and undecidability in modern physics.

I particularly liked your statement against a sort of diffused Platonism (expecially among theoretical physicists and some mathematicians): "we may believe that there is something called “the natural numbers”, N, a well-established “thing” (after all, formalized as a set) that somehow “sits there”, waiting for our mathematical tools to discover all of its properties and to prove all of its true theorems".

One comment that I should perhaps like to make, is that while I am in principle very sympathetic with this idea, I always find a bit disappointing how vaguely structural realism is spelled out in the philosophical literature. For it remains vague enough to accomodate many views which perhaps would not naturally go hand in hand. So, also in your essay, even if you indeed took a "structural" standpoint throughout all of it, I found the connection in section IV a bit unsharp. But it may well be that it is me who always struggles understanding ontic structural realism in a non superficial way.

Anyways, great essay and best of luck for the contest!

Cheers,

Flavio

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Author Markus P Mueller replied on Apr. 23, 2020 @ 12:13 GMT
Thank you, Flavio, for your comments!

I totally agree with your assessment that the details seem sometimes vague. What is "structure"? What are "patterns"?

I think that in my essay, it's necessarily somewhat vague since it's only an essay of 6 pages or so. There's only space to convey an idea, not to work it out in a serious philosophical manner.

In other literature about OSR, there are certainly more details. But perhaps some feeling of vagueness must necessarily remain. Because, once you reject a metaphysics that relies on "things" in the intuitive way (as in "habitual metaphysics", as Ladyman calls it), then you are left kind of speechless. You then have to rely on different primitive notions that are more abstract. Perhaps the idea of "real patterns" (see Dennett, for example) can makes things more concrete.

Again, I would like to read up more on it myself to get a better understanding.

Best,

Markus

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Yehonatan Knoll wrote on Apr. 23, 2020 @ 08:49 GMT
Dear Markus,

I fail to see the relevance of Turing/Godel to the accessibility of the Platonic world. Turing only showed that any single, finite machine would necessarily have a blind-spot. It tells us nothing with regard to the decidability of "whether machine M halts on input I".

As to

“[...] the history of successful novel prediction science is the most compelling evidence for some form of realism, but [...] the history of ontological discontinuity across theory change makes standard scientific realism indefensible.”

one could argue that the rational way to make progress is to `rewrite the history' of theory using a single, common ontology. This is my ambitious approach with respect to its chances of success I'm fairly optimistic by now

https://arxiv.org/pdf/1201.5281.pdf

Best,

Yehonatan

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Author Markus P Mueller replied on Apr. 23, 2020 @ 12:04 GMT
Dear Yehonatan,

thank you for your comments!

In your first paragraph, you write:

> I fail to see the relevance of Turing/Godel to the accessibility of the Platonic world. Turing only

> showed that any single, finite machine would necessarily have a blind-spot. It tells us nothing with

> regard to the decidability of "whether machine M halts on input I".

I'm not 100% sure that I understand your argument, but let me have a try:

I agree that Turing's result says something else than Gödels'. Yes, in some sense it says that single, finite machines have a "blind spot".

But it has also implications for (un)decidability. For example, it implies that there is no single axiomatic system with the following property. Consider the collection I of all inputs on which M *does not* halt. Then, for every i in I, the axiomatic system admits a proof that M does not halt on input i.

Because if such an axiomatic system existed, then we could program a machine that enumerates its provable theorems. Intertwining this with enumerating all the halting inputs would decide the halting problem. So both are in this, and other ways, related, as it seems...

Or maybe I misunderstand your message here?

> one could argue that the rational way to make progress is to `rewrite the history' of theory

> using a single, common ontology. This is my ambitious approach with respect to its chances of

> success I'm fairly optimistic by now

I agree that this might be a workable hack somehow. But are you saying that, in retrospect, we should reinterpret the *older* claims (such as Bohr's electrons) in terms of *newer* ontology? It seems like in your paper you are adopting the opposite strategy.

Best,

Markus

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Yehonatan Knoll replied on Apr. 24, 2020 @ 09:25 GMT
We are not on the same page...

What I want to say is that Turing's (and Godel's) result expresses a limitation of machines - systems which can be realized even within a classical, objective ontology.

In contrast, Bell's result expresses a limitation on the ontology: If particles were machines ("robots" in Bell's words) then his inequality would need to be satisfied (under reasonable assumptions). In my essay I define the notion of a "non-machine" to overcome Bell's limitation within a definite ontology. I argue that this new category of physical systems, which is mandated not only by Bell but even by classical electrodynamics(!) is the more generic, with machines being in some sense an `uninteresting' private case thereof.

I'm very sympathetic to your project in re.f [30]. Being under the spell of Hofstadter and Penrose in my high-school years, I also believed that was the right way to proceed. But I have since discovered the limitations of a system called Yehonatan Knoll, and that system, if it is to produce any real progress in physics, must stay as close as possible to a `pedestrian' objective ontology :)

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Author Markus P Mueller replied on Apr. 27, 2020 @ 07:56 GMT
Dear Yehonatan,

I fully agree: Turing's result is about the limitations of machines, and Bell's is about ontology. These are very different things! That's also why I believe that Goedel's theorems do not directly apply to physics (as I also write in my essay), and why my use of the notion of "structure" in both cases is not identical, but only an analogy.

About your idea of non-machines, let me hold off commenting before I finally come across reading your essay. At the end of this week, I'll have more time and should be able to start reading.

"Limitations of a system called Yehonatan...": I'm fully on board with this. :-) I'm also encountering the limitations of a system called Markus Mueller on a day-by-day basis. Perhaps the most important lesson in studying physics is to find out about one's own limitations.

Best,

Markus

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Harrison Crecraft wrote on Apr. 27, 2020 @ 12:13 GMT
Dear Markus Mueller:

I very much enjoyed your essay. It closely parallels ideas in my essay, in which I distinguish between empirical models and conceptual models. An empirical model, like your description of theory, describes objects of observations and their empirical relationships. A conceptual model, like your structure, describes what the theory is talking about, i.e. it tries to...

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Author Markus P Mueller replied on May. 4, 2020 @ 14:06 GMT
Dear Harrison (if I may),

thanks very much for your thoughtful comments!

I really like your insight that "being undifferentiated" can also mean that something is defined in a contextual way. Your example with reference frames in SR is a very good example.

I would like to find out more about your view on QM (especially what you mean by DDCM), and will try to have a look at your essay if I manage to find the time.

Best,

Markus

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Fabien Paillusson wrote on Apr. 29, 2020 @ 10:48 GMT
Dear Markus,

This is a very insightful and very well written essay you have got there!

The structural realism you put forward coincidentally resonates with some of my recent readings on Poincaré who was also advocating for a form of structural realism well before quantum mechanics.

A naive query I would have about an ontology based on structure is that it seems to rely on a form of first order logic where predicates, and the rules they may obey, are what remains when what they can act on is forgotten. But I cannot help wonder how would that work if the predicates themselves are instantiations of models in higher order logics; it would seem to run into a form of infinite recurrence of Russian dolls structures that in some sense never stops; unless we select a given model or order of logic.

I would be interested to read your thoughts on this :) .

In case you would be interested I develop a similar view in my submitted essay where, as far as I understand your perspective, we claim that finding meaningful differentiations within a given structure (of observational phenomena for example) is in fact a defining feature of scientific practice https://fqxi.org/community/forum/topic/3477 .

Best of luck for the contest.

Fabien

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Author Markus P Mueller replied on May. 4, 2020 @ 14:47 GMT
Dear Fabien,

thanks so much for taking the time to read my essay, and for your comments!

It’s very interesting to hear that Poincare was already advocating for some form of structural realism. Off the top of your head, do you perhaps know a reference for this? I’d be curious!

Now, regarding your question on the “Russian dolls structure” in an ontology of structure. First, note that answers to your question — more generally the question of how to think of an ontology of structure, and how to define it much more carefully than in my essay — can be found much better in the works of philosophers who have written about this in much more detail. My favorite source is still Ladyman.

Now, second, I guess that the way I understand “structure” is different from how it is used in your argument. I totally agree that there is this infinite-recurrence problem that you describe — if one relies on a view in which we have “mathematical objects” (the individuals) and their “relations” (the predicates etc.), and that an “ontology of structure” means to drop the former and keep the latter.

But this is not how I want to understand “structure”. Rather, I’d use “structure” as the whole package of what a given consistent formal system, or theory, talks about. It is what all models of a given theory have in common.

This is vague for two reasons. First, because for the essay I didn’t do the hard work one would have to do to make this philosophically and mathematically more rigorous. Second, I believe that it *must* appear vague to some extent because our intuitively “most concrete” ideas are those of things and their properties, and these notions are exactly what’s avoided here to begin with.

Good luck for the contest to you, too!

Best,

Markus

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Member Dean Rickles replied on May. 12, 2020 @ 07:46 GMT
Hi Markus.

Poincare's stucturalism is found in his Science ad Hypothesis. There was a whole bunch of other related stucturalisms too, of Russell, Eddington and others, aiming to get an isomorphism between our experience of the world and the world itself. Things beyond the structure had to go, at least from the point of view of science's scope. My essay is slightly similar to yours in that it ultimately ends up pushing towards some kind of structuralism (though I don't quite call it that).

But, given the every thing must go approach, there is a potential problem with structural underdetermination that various dualities seem to pose: these are structurally different, yet would generate what seem to be the same phenomena [e.g. AdS/CFT]. This would pose problems for your view since we then face the same question as for things: which structure is being observed? How might you deal wth this, assuming it's valid?

(My essay is here: https://fqxi.org/community/forum/topic/3450)

Best

Dean

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Author Markus P Mueller replied on May. 14, 2020 @ 13:27 GMT
Hi Dean,

ah, excellent, thank you for the reference! I'll have a look at it, and will also see what Russell and Eddington had to say.

And thank you for your thoughtful comment on structural underdetermination! I would say that this all depends on what we exactly mean by "structure" -- a question that I haven't tried to answer in detail in my essay (I've kept it somewhat vague). In AdS/CFT, for example, depending on the answer to this question, one could either say that the boundary CFT and the bulk gravity theory are different structures, or that they are the same. It depends on what kind of notion of "equivalence" of structures we accept.

However, I think here we are in a better position than in the context of "things": while a "thing" is usually imagined as a kind of god-given entity with clear boundaries, we have quite a few different options to clarify what we mean by "a given structure". Hence I'm optimistic that the question of "which structure" (that you posed) could be clarified. But more work would be needed (and has probably been done by the philosophers).

Best,

Markus

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Michael James Kewming wrote on May. 3, 2020 @ 07:26 GMT
Hi Markus,

I enjoyed reading your essay. You present some an interesting an very unique perspective.

If I understand correctly, you are proposing we focus on the structural patterns between elements of physical theories. That is, the relationships between things in the theory are fundamental, not the things themselves? Is this what you meant by real patterns? It was a little vague.

If I have understood this correctly, I do believe I could get behind this idea with a bit more convincing. There are considerable overtone in your essays to the structuralist ideas of contemporary philosophy which I have been somewhat sympathetic too. I think it might provide some useful insights for the physical sciences.

In any case, I will be checking out a few more of your papers on this topic!

Thanks again,

Michael

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Author Markus P Mueller replied on May. 4, 2020 @ 14:18 GMT
Dear Michael,

thank you for your comment!

I agree that the notion of "structure" in my essay is a bit vague. One would have to invest more work to make this mathematically and philosophically sound.

What I do *not* mean by "structure" is simply the relations between things (in the sense, for example, of Newman's objection). What I rather mean is, basically, whatever we can say about the "real patterns" we encounter.

Ladyman at al. have clearer definitions of this. They write, for example, that certain patterns behave like "things". But the notions of "things" or "relations" are not taken as primitives to ground the notion of pattern or structure.

Thanks again for checking out my essay!

Best,

Markus

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Yutaka Shikano wrote on May. 4, 2020 @ 23:37 GMT
Hi Markus,

Congratulations to the well-organized essay. I learned so many quantum foundations topics from this. In your quantum-optimistic hypothesis, how to deal with the data-driven science to be approached to quantum mechanics? On quantum mechanical objects or events, this seems to NOT be reproductive even by the future AI technology if this hypothesis is true.

Best wishes,

Yutaka

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Author Markus P Mueller replied on May. 14, 2020 @ 13:31 GMT
Hi Yutaka,

good to hear from you, and thank you for your comment!

I would say that the fact that a given event cannot be predicted even by future AI (if I understand your suggestion correctly) is a good thing -- at least if you want to rely on quantum cryptography, for example. :-)

Of course, this doesn't mean that data-driven science or computation cannot tell us anything new about quantum mechanics. Even learning the quantum-mechanical properties of large systems seems to be something where such science, and perhaps AI, can be immensely useful

All the best,

Markus

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Gemma De las Cuevas wrote on May. 5, 2020 @ 14:18 GMT
Dear Markus,

Thank you so much for writing this essay. I enjoyed reading it very much, and learned a lot of stuff. I think the message is somewhat orthogonal to my essay, but not necessarily contradictory. I like your viewpoint regarding how we implicitly assume there to be a metaphysics of things, and how this may be mistaken.

Thanks again, and all the best,

Gemma

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Author Markus P Mueller replied on May. 14, 2020 @ 13:36 GMT
Dear Gemma,

thanks so much for your kind words! I'm glad you enjoyed the essay.

I believe that our views are not really orthogonal, they are just emphasizing different aspects. I fully agree that "undecidability is everywhere". Whether we see this as a limitation (for example, we cannot predict all aspects of some system) or as a positive outlook (differentiation is everywhere) may be a matter of perspective.

Hope to discuss this in person once the crisis is over!

Best,

Markus

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Hippolyte Dourdent wrote on May. 6, 2020 @ 12:48 GMT
Dear Markus,

I really enjoyed reading your essay, and I sympathize with a lot of your ideas.

Especially, the fact that letting go of the concept of "things" and acknowledging that some questions have no answer, "dissolve" the paradoxes and avoid the invocation of weird ontological phenomena. Indeed, quantum theory invites to consider the notion of "entities" (as they were defined...

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Author Markus P Mueller replied on May. 15, 2020 @ 11:37 GMT
Dear Hippolyte,

thanks so much for your kind words, and for your detailed comments!

I agree that there is a big difference between Spekkens’ view and QBism. Seeing the quantum state as some kind of incomplete knowledge is very different from seeing it as an agent’s belief, and there are many more differences between these views. Still, I think that they have something in common: they see the quantum state as something that pertains to some notion of observer which is seen as holding incomplete information in some sense. Hence, both views express the hope that more can be said about the part that is not known to the agent that assigns the quantum state, presumably about some underlying reality: either by finding a kind of plausible “causal” ontological model, or by understanding what the Born rule has to say about the world on which we place bets.

I also agree that the word “structure” is ambiguous. I guess there are two reasons for it: first, this is only an essay, and I didn’t do the hard work to make this notion mathematically or philosophically sound or fully concrete (the structural realists among the philosophers have more to say about this). Second, however, it must *seem* vague to some extent: after all, what we would intuitively label as our most “concrete” understanding is naturally in terms of *things* — and this is a view that is explicitly rejected here.

I will try to have a closer look at your essay, the abstract sounds very interesting!

Best,

Markus

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Malcolm Riddoch wrote on May. 8, 2020 @ 01:07 GMT
Hi Markus,

your essay is definitely my top pick for this contest, thank you for contributing! You state in your concluding hypothesis:

“The quantum world is probabilistic structure. In other words, it is not a “thing” or a collection of things, but it is the multitude of statistical patterns and their structural relations that any observer encounters in their data.”

So...

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Author Markus P Mueller replied on May. 15, 2020 @ 14:10 GMT
Dear Malcolm,

thanks a lot for the thoughtful and fun comments! I’m glad you liked my essay.

You write: “And for you might this ontic structural – quantum – realism also be a form of wave function realism where the quantum side of that realism equates to a pure potentiality for experience rather than a thing-like external quantum world?” Yes in fact! I’m stunned that you...

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Malcolm Riddoch replied on May. 18, 2020 @ 04:23 GMT
Hi Markus,

“To say what a pattern is, you have to choose a compression algorithm, or a universal machine (which is analogous to a choice of language). For finite data, the notion of compressibility will depend on this choice. Any ultimate definition of a real pattern will have to deal with this issue in some sense…”

I can see how this might be a practical problem in choosing...

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adel sadeq wrote on May. 9, 2020 @ 18:01 GMT
Dear Markus,

Your essay is one of the few that I could identify with. While I am not very sure of how close our views are it seems we agree that reality is computable. My model sort of points outs that nature is a mathematical structure that represents probability structure as in "geometric probability", also taken line-line or circle-line picking as examples. you can see that the expectation value characterizes the "process", I would guess similar to you idea. Moreover, when I interpret the line lengths(after some summing procedure and inverting and normalizing) as energy many results that agree whith QM and QFT is obtained. Also my model sort of agrees generally with

https://www.physicsforums.com/threads/the-thermal-interp
retation-of-quantum-physics.967116/

I hope you are discouraged by my low score, since I am not into political chit chating just for the score. Thanks

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adel sadeq replied on May. 9, 2020 @ 18:06 GMT
I hope you are discouraged by my low score, since I am not into political chit chating just for the score. Thanks

of course that shout read

I hope you are NOT discouraged by my low score, since I am not into political chit chating just for the score. Thanks

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Satyavarapu Naga Parameswara Gupta wrote on May. 11, 2020 @ 16:04 GMT
Dear Professor Markus

I got a very nice introduction to you from Prof. Malcolm Riddoch, this post is about furthering that discussion...

This will give me a fundamental approach to the quantum mechanics. I will go thro' your essay soon of them and contact back to you ASAP.

I mainly worked in cosmology , I am yet to enter into the world of Quantum Physics, i will do that in...

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Satyavarapu Naga Parameswara Gupta replied on May. 16, 2020 @ 09:14 GMT
Dear Professor Markus

Hope you will have a visit to my essay, before time expires

Best

=snp

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Chandrasekhar Roychoudhuri wrote on May. 12, 2020 @ 01:42 GMT
Dear Mueller:

Excellent scholarly article.

I basically agree with your views:

“I argue to replace this perspective by a worldview in which a structural notion of ‘real patterns’, not ‘things’ are regarded as fundamental. Instead of a limitation of what we can know, undecidability and unpredictability then become mere statements of undifferentiation of...

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Author Markus P Mueller replied on May. 15, 2020 @ 14:38 GMT
Dear Chandra,

thank you for your comments!

Let me ask a clarification question. When you point out that we are "information limited", are you then saying that this will forever prevent us from getting any "final answers" about reality? In the abstract of your essay, you seem to argue the other way: that we can make progress nonetheless.

You also write: "Unlike Copenhagen Interpretation, we do not need to give up visualizing ontological reality." So are you claiming that there is an underlying reality in the usual hidden-variable sense, and that we can get our hands on it?

Best regards,

Markus

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Eckard Blumschein wrote on May. 13, 2020 @ 09:08 GMT
Dear Marcus Mueller,

Essays on top of community ranking tend to not even notice those who are ready to fundamentally justify the wave function and the redundant FT as a fundamental of it.

I nonetheless very much enjoyed reading your anti-agnostic worldview which I share in principle. I thank you very much for reminding of Euclidean geometry which I understand as a special case of the elliptical one. Isn't use of mathematics often too less or inappropriately differentiated? To me the denial of distinction between past and future implies an unjustified arbitrary choice of the reference point which may cause confusion.

I would like to see you on top of ranking and also on job even in case Kadin will not be quite wrong.

Eckard Blumschein, an old Berliner

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Author Markus P Mueller replied on May. 15, 2020 @ 14:46 GMT
Dear Eckard Blumschein,

thank you for your comment! Honestly, I don't quite know what to make of it... but I thought I'd send you best wishes to Berlin, where I've lived for several years.

Best,

Markus

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Eckard Blumschein replied on May. 17, 2020 @ 04:46 GMT
Dear Markus Mueller,

I just tried to elaborate on what I directly indicated with be careful when calculating as if. Please find possible implications concerning QM yourself.

Incidentally, I live for many decades in Magdeburg.

Best, Eckard

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Irek Defee wrote on May. 13, 2020 @ 09:28 GMT
Dear Markus Mueller,

Your essay is extremely well written with sharply presented arguments. One can agree that the world which is open for opportunities (unpredictable) provides generally optimistic perspective though sometimes reality bites painfully as one can see. Questions which remain are of deeper foundational nature: why it is as it is, e.g. your hypothesis about the quantum world. It has to be originating from an underlying structure unless one accepts that every possible world exists and we just happened in this one.

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Author Markus P Mueller replied on May. 15, 2020 @ 14:55 GMT
Dear Irek Defee,

thanks very much for your kind words!

I fully agree: it makes sense to have a generally optimistic perspective, but sometimes reality bites painfully.

About the quantum world: yes, many different views are possible, and I'm not claiming the final word on this. The questions of "why these laws of nature and not other ones" and "how to think about all possible universes" are deep, hard and far-reaching, and I'm not trying to say anything about this in my essay.

Best,

Markus

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James Arnold wrote on May. 13, 2020 @ 15:05 GMT
This is a thoroughly brilliant essay. It offers, if not optimism, a palliative to even the most realistic of scientists.

In my essay I offer a perspective that is even more optimistic: The world is inherently spontaneous (not random and not determined), which is why we observers are inherently spontaneous, and that is why knowledge can only be tentative and limited. The world is not strange, but rather, like us, it is wonderful.

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Author Markus P Mueller replied on May. 15, 2020 @ 15:06 GMT
Dear James Arnold,

thanks very much, I'm glad you liked my essay!

I have some sympathy for your view of quantum events as spontaneous -- it paints a quite vivid picture, and points out that it is not just about "uncontrollable external perturbations". But can your view also be coined in the more familiar terms of "intrinsic randomness"?

Best,

Markus

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James Arnold replied on May. 16, 2020 @ 12:35 GMT
The idea of actual, physical randomness is an odd one. If it isn't meant to be due to a complex of unrelated extrinsic causes, to be extrinsically uncaused, and intrinsically foundationless, would be the best explanation for nothing happening at all.

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Member Tejinder Pal Singh wrote on May. 14, 2020 @ 09:33 GMT
Dear Professor Mueller,

It was a pleasure reading your beautiful essay, whose overall philosophy I agree with. I fully support redefining and reinterpreting realism to make it in accord with what physical theories present us.

With regard to quantum mechanics, my view is that the unpredictability and indeterminism are not fundamental. Rather they emerge as apparent effects when an underlying deterministic theory is coarse-grained. I explain this in my new arXiv preprint

Nature does not play dice on the Planck scale

and also in my essay in this contest. Hope these will be of interest to you.

My thanks and best wishes for your success in this contest.

Tejinder

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Author Markus P Mueller replied on May. 15, 2020 @ 15:24 GMT
Dear Tejinder,

thanks a lot for your kind words!

Let me ask you a question on your approach. If dynamics at the Planck scale is fully deterministic, and coarse-graining leads to quantum mechanics, then Bell's theorem implies that this dynamics must be non-local (as you also point out in your paper). But if it's non-local, an immediate worry would be that it leads to superluminal signalling. Is it clear that the coarse-graining in your model removes the possibility of signalling?

Best,

Markus

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Member Tejinder Pal Singh replied on May. 15, 2020 @ 17:12 GMT
Thank you Marcus, for asking an important and interesting question. I try to explain what I mean by non-locality in this matrix dynamics, and why it does not imply superluminal signalling. In this dynamics at the Planck scale, there is no space-time. There is only a new notion of time - the Connes time. All processes take place in a Hilbert space, where there is no conventional notion of distance...

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Member Emily Christine Adlam wrote on May. 16, 2020 @ 08:52 GMT
I really enjoyed this essay. Relating the incompleteness theorem to Euclid's axiom is a great illustration of the point which really puts the issue of incompleteness in a new perspective. And I agree that much of our trouble with the interpretation of quantum mechanics comes from asking the wrong questions and attempting to force the theory into an over-specific ontological structure.

I wondered about your phrasing of the 'unanswerable questions' in quantum mechanics - 'What is, at some given moment, the actual configuration of the world?' Relativistically the concept of 'the state of the world at some given moment' isn't well-defined, so it would seem that it follows directly from relativity that this question is unanswerable, and therefore quantum mechanics wouldn't be adding anything very new here. Or did you mean 'at some given moment' to refer to 'on some spacelike hyperplane of simultaneity'?

I also think there's an important difference between the case of quantum mechanics and the case of 'the same time.' In the case of relativity, Einstein did not simply assert that it so happens that questions about 'the same time' have no answer - he argued convincingly that these questions are meaningless (in our universe and in a large class of universes like ours). Whereas quantum mechanics doesn't seem to show us that 'What is the actual configuration of the world (on some suitable spacelike hyperplane)'? isn't a well-posed question - rather it's just a contingent fact that in our actual world this question has no answer (if it is indeed a fact!). So the claim that this question is unanswerable seems less logically compelling then the claim that 'same time' questions are unanswerable (though of course that doesn't mean it isn't true!). I wondered if you agree, or if you think there's a stronger claim to be made to the effect that questions about the actual configuration of the world aren't even meaningful?

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Author Markus P Mueller replied on May. 26, 2020 @ 13:05 GMT
Dear Emily,

I perfectly agree, regarding the question "What is, at some given moment, the actual configuration of the world?". Strictly speaking, relativity of simultaneity says that this formulation needs to be supplemented with more details to make it well-defined. As you point out, one way would be to state this relative to some spacelike hyperplane of simultaneity.

What I had in...

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Cristinel Stoica wrote on May. 17, 2020 @ 05:02 GMT
Dear Markus,

Brilliant essay, I liked the structure of arguments, the ideas, and the general gist of it. The sensation is that of regaining a freedom considered lost. It may be enough that always exists in a mathematical sense a possible structure that fits all the data, like in Wheeler's version of the twenty questions game. It may also worth trying to fit a solution that is unitary, i.e. unbroken by projections, this is one of the things that interest me (such a solution can't be fixed just by any initial conditions at a given time, it depends on future experimental settings). Best way is to keep open all possibilities. Thanks for the essay, it was a pleasure to read it!

Cheers,

Cristi

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Author Markus P Mueller replied on May. 26, 2020 @ 13:22 GMT
Dear Cristinel,

thanks very much for your kind comment! I’m looking forward to reading your essay too — it’s sitting here on my desk, waiting for the next round of fun readings after a marathon of journal refereeing. :)

I also enjoyed your online talk in our seminar. Let’s hope that these strange Corona times will soon be over, and we can have meetings in person soon again!

Best,

Markus

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Member Christopher A. Fuchs wrote on May. 17, 2020 @ 20:03 GMT
Dear Markus,

I very much enjoyed your thoughtful, masterfully written essay. It was so refreshing with its message of hope in comparison to all the usual discussions that want to turn back the clock of quantum mechanics to something more akin to classical physics or, metaphorically, Hilbert’s program.

Years ago (22 or so!), I wrote a job application which I’ve just looked up. ...

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Member Tejinder Pal Singh replied on May. 18, 2020 @ 09:13 GMT
Dear Professor Fuchs,

There is no experiment that contradicts quantum mechanics to date. However, quantum mechanics has been tested and verified only upto TeV energy scales or so. Thus when we try to make theories of quantum gravity valid at the Planck scale, we can make them by assuming that quantum theory holds at the Planck scale. Or we can make them by assuming that quantum theory is violated at the Planck scale, but recovered at lower energies. Then, if the predictions of the two approaches are different, experimentalists can try to find out which approach, if either one, is correct.

I hope we can agree on this much.

It could well be that dynamics at the Planck scale is deterministic; yet the emergent low energy dynamics, being QM, is indeterministic:

Nature does not play dice at the Planck scale

But of course this deterministic Planck scale dynamics is not a return to Newtonian days: it is a non-local, non-unitary matrix-valued Lagrangian dynamics. There is no space-time here: space-time, along with quantum mechanics, are emergent.

Thanks and best regards,

Tejinder

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Author Markus P Mueller replied on May. 26, 2020 @ 16:04 GMT
Dear Chris,

I’ve just seen your comment today, after several days offline. I am delighted that you find my essay meaningful — it really means a lot to me!

The excerpt from your job application is a beautiful expression of such a more positive view. I couldn’t agree more! And thank you for pointing me to (your transcript of) Wheeler’s notes. This is fascinating, and I will give your paper another read. It strikes me as very much in the spirit of what I’ve tried to describe, although (as you already wrote) it’s not quite what I had in mind. I’d see the relation between Goedel undecidability and quantum unpredictability more as a conceptual analogy rather than as a direct relation in the way Wheeler seems to have had in mind there. Still, this is fascinating!

“Normative structural realism” seems like a great idea to me. I’d love to discuss it offline with you! Up to differences in several details (of course), this seems like a concept that could perhaps describe core ideas of QBism, and at the same time fit well some of my own views. In my long “law without law” paper, for example, I argue for something that I initially motivate as some kind of objective first-person chances. However, this is not really about “objective probabilities”, but rather about the collection of valid priors which any observer may choose and update (I also name QBism as an influence in formulating it this way). In this sense, the world “is” the structure that tells you how you ought to update your beliefs (which is a weaker claim, for example, than the objective numerical probabilities that orthodox QM-views tend to postulate). In any case, I’m just typing this spontaneously, and there would be much more to think about and discuss.

Thanks again so much for your great comments! Stay safe, and let’s hope that the crisis will soon be over and allow us to meet and chat in person soon.

All the best,

Markus

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Jenny Wagner wrote on May. 18, 2020 @ 11:57 GMT
Dear Professor Mueller,

thanks a lot for these great insights and new viewpoint!

While reading, I was tempted to compare your viewpoint to objective programming. If your structure S defined in Fig. 1 is an abstract class, we cannot derive specific instances from it and thus, without an instance at hand, we cannot give answers to certain questions about S.

I hope to be able to apply your ideas to my special case of under-constrained problems in cosmology as well.

All the best for the contest and your future research!

Jenny Wagner

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Author Markus P Mueller replied on May. 26, 2020 @ 16:10 GMT
Dear Dr. Wagner,

thanks a lot for the comments. I like your comparison to object-oriented programming! Perhaps there is more to be learned (and more transparently so) by using this analogy.

It would be fascinating if such ideas could have any use in cosmology. It is a field that I follow with great interest, but I'm not at all an expert in.

Good luck for your research and your essay, too!

Best,

Markus

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Member Robert W. Spekkens wrote on Jun. 24, 2020 @ 15:28 GMT
Hi Markus,

I really liked your explanation of the philosophical significance of the incompleteness theorem, namely, that incompleteness of a theory signals that there are statements that cannot be proven nor disproven simply because the axioms that would allow one to generate such proofs are not present (or, equivalently, the theory can be differentiated and the status of the statement is...

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Author Markus P Mueller replied on Jul. 17, 2020 @ 08:53 GMT
Hi Rob,

thank you so much for your kind comments! I'm glad that you liked my essay. Let me begin by apologizing that I have used "Spekkens-like interpretations" in a way that may misrepresent your own view. I'm of course well aware that you do *not* see the world in that way, and that you'd rather regard causal structure as primary. I'll clarify this as soon as I get the chance (in version...

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