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Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020)
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Undecidability and unpredictability: not limitations, but triumphs of science by Markus P Mueller
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Author Markus P Mueller wrote on Apr. 21, 2020 @ 11:12 GMT
Essay AbstractIt 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 BioMarkus 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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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 getting to know what's there to know at all.
This bears some similarity to what
Karl Svozil has called the 'third path' in dealing with these notions: most of the time, the issue is either neglected as an artifact, an esoteric mathematical rumination not more relevant to the (physical) world than the precise number of angels on the head of a pin, or on the other extreme, enlisted into grim pronouncements of our doomed quest for knowledge. Trying to find a third (or perhaps 'middle') way of taking it seriously, even as the starting point of some constructive challenge to outdated ideas that force us to engage with some core assumptions is a welcome change of pace.
Before I go into deeper discussion, however, I'd like to ask a question, if I may. The sort of structural realism you champion derives from a venerable tradition, stretching back at least to William James, Bertrand Russell, and Arthur Eddington. But it seems to me that a challenge raised against such views by the mathematician Max Newman (known these days generally simply as 'Newman's objection') hasn't really found a good answer. That challenge essentially consists in pointing out that if everything you know about some domain is the relational structure it fulfills, then really, all you can answer are questions of cardinality---for if there's the right number of elements, any structure will fit, so to speak.
Do you think that's a problem for your view? If not, how do you propose it is overcome, or why doesn't it apply?
Best of luck in the contest!
Cheers
Jochen
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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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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 particular versions of structural realism to which it would apply. But here's how I understand it in the spirit of the view sketched in my essay.
Yes, if you take some large enough domain, you can put any structure on it. But consider the conclusion: that all we can make, in effect, are cardinality claims. The formulation of this conclusion already indicates the limitations of Newman's argument: it assumes that there is a ``domain of things'' that could be counted, and "structure" is simply a notion of relations in set-theoretical terms.
However, the view that I've sketched would exactly deny this. What I mean by "structure" is something much more general: anything that a consistent theory talks about -- not necessarily a "set with relations". In particular, it is nothing that would supervene on a "collection of objects".
I think that this is also the reason why, as far as I understand, Newman's objection is typically used as an argument against *epistemic* structural realism, not *ontic* structural realism as I (and much more deeply, Ladyman) defend it. In the former case, you can think of the world as a collection of "real things" (for example particles), but we have no access to these directly. Based on this metaphysical assumption (that I reject), a set-theoretic understanding (a mathematical notion of relations with no physical primacy) is natural, and Newman's objection seems perhaps applicable.
What I'm saying here is probably much more deeply analyzed by the supporters of ontic structural realism. I'd like to read more about that.
Thanks again for your comments on my essay! I'm looking forward to reading yours.
Best,
Markus
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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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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 the same predictions. Essentially, you can mirror one theory within another---roughly, via something like a Gödel numbering, but more explicitly, if you have a theory which allows for universal computation, you can just 'code up' a simulation of whatever other theory you want to say gives the 'right structure' within the former.
Say you've got a fully worked-out version of string theory, and want to claim that hence, that gives you the full 'real structure' of the world, and with that, everything that can be said about it (in the sense of everything there is to be said). But then I come along, and encode string theory into some electromagnetic field configuration that corresponds to a computer's memory containing a program that simulates string theory with some initial conditions, and derive all the same predictions from (presumably rather complicated) calculations using nothing but Maxwell's equations---in what sense, then, is the structure of the world that of string theory, and not that of Maxwell's electromagnetism? (Apologies, by the way, if you address this in your essay, unfortunately I still haven't gotten to digesting it fully.)
Of course, there's going to be more structure than just the Maxwell equations, corresponding to some complicated initial state, but there's presumably some initial state in the string theoretic description too, plus there will be very many programs on many different computational architectures---many different field configurations---leading to the same predictions.
But I'd need some time to make this thought more precise. I think I'm otherwise quite happy with accepting OSR as a live option---I've in a sense chosen the other way out: rather than conclude that structure is all there is, I presume that what there is will always outrun our ability to fully describe (which description, I agree, is essentially structural), largely motivated by something like the above worry on structural underdetermination (regarding the question of
implementing a computation).
I'll hold off on further comments until I've gone through your essay. I can say already, however, that it's excellent, and deserves to go far in this contest.
As a final remark, I've found many articles of Svozil highly illuminating on this topic. I think he's in Vienna, too, no (albeit at the TU)? Maybe you should strike up a discussion and see if you find some common ground!
Cheers
Jochen
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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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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
things, but rather, it is given by a web of
relations."
Back then, I appealed to a notion of 'relative facts' to encompass roughly what you call 'differentiations' of a structure---the idea being that the questions not answered by a given structure have answers only relative to other events, sort of like an electron's state is 'spin up' relatively to a measurement apparatus' registering the appropriate measurement, whereas to you, I gather, the 'spin up'-value would be a further differentiation of the structure giving the system's state.
One worry, to me, is then how differentiation happens. If we, say, make a measurement on a quantum system, to stay with the example, does this then entail a literal further specification of the state---i. e. does the structure go from S in which the question of the electron's spin is indeterminable to S' in which it has a definite answer? If so, that seems hard to square with a purely structural reading---for if there were some further structure that determines what value is provided, then we simply didn't have the full structure to begin with (something which will be hard to square with the various limitative theorems of QM).
But on the other hand, if differentiation happens essentially randomly, then that process does not have a formulation in terms of structure---so in a way, considering this as a structural view is like having a 'computational' universe that every now and then has to look at an oracle to draw a genuinely random bit from a hat.
The third alternative would be to go to a kind of 'many worlds'-view, where all differentiations already exist---something like the 'relative facts'-version. But it seems questionable whether that's then still a 'structural' view---after all, if we have some structure S, allowing for differentiations S' and S'', and we say that those differentiations are already out there---say, again, in the two distinct possibilities of an electron's spin value in a superposition---then these differentiations, from the point of view of us who only have the description according to S, take the role of the 'things' that the structure is a structure
off, and an experiment will tell us which it is---although of course, it will yield both answers.
Regardless, I think your criticism of 'thingism' is apt, on the whole---I've been trying to steer a kind of 'middle way', having become skeptical that pure structure can yield enough of a world to ground our experiences, but all my conclusions there are very tentative. I don't believe that there's a world of 'fundamental' facts that's simply given to us, a container of stuff to discover; but I'm also not sure that the mere specification of relations does not leave it just all empty, so to speak.
Anyway, I think this is an intriguing topic to explore. You may actually find some congenial notions in my essay this year, and the
Found. Phys. article that spawned it---while I agree that Gödel's results, as such, don't have applicability to the physical world, they, together with a great many other similar ideas---the unsolvability of the halting problem, Russell's paradox, and others---are really a manifestation of a more general structure, captured in a fixed point theorem due to F. W. Lawvere. This I try and connect with the measurement process in quantum mechanics, in a way which seems very apt to your idea of 'differentiation'. I view it slightly differently, based on additional considerations, but I believe the framework fits.
Cheers
Jochen
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Author Markus P Mueller replied on Apr. 23, 2020 @ 13:03 GMT
Dear Jochen,
thanks for your reply. The time you take for this is highly appreciated!
Before going into details of what you write, I think that the answer to many of your comments is: it depends on what we mean by "structure". In my essay, I'm not really defining it properly (in particular in the section on the physical world). Any serious philosophical approach that tries what I've...
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Dear Jochen,
thanks for your reply. The time you take for this is highly appreciated!
Before going into details of what you write, I think that the answer to many of your comments is: it depends on what we mean by "structure". In my essay, I'm not really defining it properly (in particular in the section on the physical world). Any serious philosophical approach that tries what I've sketched will have to give a clear(er) definition. Also OSR has to do that (and I suspect that it does, but they mean something slightly different from what I mean).
Regarding your example of the Maxwell's equations and String Theory, I think that what this tells us is that we should define "structure" in terms of "big enough equivalence classes", or admit "coarse enough isomorphisms" when we define it. In particular, there may be two theories T and T' that talk about the same structure S. I would say that your example of Electromagnetism (i) and String Theory (ii) is of that kind: two theories that give the *same* structure.
Being a structural realist in *that* sense, I'd say that there is no ontological difference between the statements that "(i) is true" and that "(ii) is true". But I admit that this does not really come across in my essay, because I'm not giving a clear-enough definition of "structure". And there are many questions that such a view leaves open.
You are right that it would be nice to talk more to Karl Svozil; I've only met and chatted with him once, and he seems to have many clever ideas and insights that touch these topics.
But I'd also find it nice to meet you in person at some point in the near future. Perhaps I can invite you to visit IQOQI when the Corona crisis is over? It would be a lot of fun to chat in person! Also, we have a regular Physics-Philosophy-Meeting here that you might enjoy.
Now, regarding your second email and quantum mechanics:
Again, I was clearly not detailed enough to say what I mean by structure or differentiation in this context. That is certainly a drawback of my essay (also due to space limits, of course, but also I don't really know how to do the definitions properly -- it's more an idea than something fully worked out.)
Here's what I do *not* mean. I don't mean to say that the world now is structure S, and once we learn an additional measurement outcome, it evolves into a more differentiated structure S'.
Instead, consider the quantum world on all of spacetime. There are certain "real patterns" in accordance with quantum physics: for example, certain events that happen earlier on (perhaps "preparations") are in correspondence with frequencies of certain types of events later on (correlations with "measurement outcomes"). This would be structure S.
A more differentiated structure S' would be the world according to de Broglie-Bohm theory: additional (unobservable) events earlier on that are deterministically correlated with outcomes later on. The corresponding theory T' makes more claims than T, and so S' would be more differentiated than S.
In other words: I'm just saying that views in which quantum probabilities are not "knowledge *about* the world" are in some structural sense less differentiated than view in which they are. So a structural view may increase one's confidence to accept views of the former kind.
I'm really curious to find out about your "middle way", but I'll postpone commenting on it until I have read your essay. I'm having a busy time with some deadlines next week, but I'm eager to read your essay directly after that.
Best,
Markus
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Jochen Szangolies replied on Apr. 25, 2020 @ 14:54 GMT
Dear Marcus,
I have you to thank for engaging with my comments in such an open way! These contests are always at their best when they stimulate frank exchanges on views that may go slightly beyond what one would normally put into a journal article or the like.
And I'd very much like to come for a visit to Vienna---although thinking about traveling plans seems almost frivolous these...
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Dear Marcus,
I have you to thank for engaging with my comments in such an open way! These contests are always at their best when they stimulate frank exchanges on views that may go slightly beyond what one would normally put into a journal article or the like.
And I'd very much like to come for a visit to Vienna---although thinking about traveling plans seems almost frivolous these days. Perhaps one lesson we could take away from the present situation is that we should try to create more and better avenues for online exchange of views---something like virtual research/discussion groups, where people interested in some topic can congregate, discuss with either live-sessions or in a chat/forum based manner, exchange drafts for articles/request comments and the like. Could be as simple as a Teams channel, or something like that.
But back to the things themselves, as Husserl said---or to their absence, as it were. Regarding the 'modding out' of equivalences between structures, I'm afraid that this might leave us with altogether too little in the way of substance to account for the world and out experience within it---if we agree that in my example, electromagnetism and string theory yield in some sense the same structure, then one could also draw in all manner of 'different' systems---say, for example, the three body problem is at least conjectured to be computationally universal, so you could encode the requisite data into its initial configuration, and then just let Newton's laws do the rest. Or, of course, any other theory that allows for universal computation.
So fine, one might try to say that then, most of the structure is in the initial condition---the program, so to speak. But this, too, is far from unique: you can instantiate the three body problem with all manner of initial states, implementing different Turing machines that then instantiate the requisite computation from different initial conditions. In each case, that would add some constant number of bits to the length of the initial program, corresponding to the specification of a Turing machine to be simulated.
So suppose that you have an initial condition for the three body problem that can be specified using n bits, such that the resulting system implements the 'structure of the world' in some sense, by essentially implementing some Turing machine T executing the n bit program. Then, it seems to me you could find a TM T' such that it takes at most n + O(1) bits input to implement the same program, with the O(1) factor corresponding to T' simulating T. But then, have you really said more about the world other than 'it contains at least n bit of information' if you specify its structure in this way?
I think this is essentially the Newman problem again. In some sense, all 'universal' structures---structures corresponding to theories allowing for universal computation---are equivalent: whatever you can describe using one, you can describe using another, with at most some constant overhead.
Maybe one could try to argue for parsimony, and single out that structure which yields the most compact specification---which has the problem that the question which one this is will be undecidable, due to the uncomputability of Kolmogorov complexity. Or, one could try to adapt the various attempts at solving the threat of trivializing computationalism---because that's essentially the same problem, again: virtually every system can, naively, be viewed as instantiating virtually every computation. There are, I think, certain avenues regarding dispositional/counterfactual/causal accounts of computation that one could pursue, in order to arrive at a notion of isomorphism between structures that's coarse-grained enough to allow for the identification of 'obviously identical' structures, without being so coarse-grained as to trivially identify virtually all structures with one another. I'm not sure if that'll work, but, with a more careful fleshing out of the notion of structure, I think there's at least a few avenues to explore here.
Regarding the concrete application towards quantum mechanics, I think I understand your proposal somewhat better now; but if the structure, as such, only accounts for the correlations in measured data, then how are concrete measurement outcomes accounted for? Pre-measurement, only a certain probability distribution over outcomes exists, but post-measurement, we at least seem to have observed one definite outcome.
Now, I suppose one way to account for this without appealing to some sort of coming-into-being of a more differentiated structure is to appeal to a sort of facts-as-relations account: before the measurement, relative to the '|ready>' state of the detector, the (say) qubit is in an equal superposition; after the measurement, relative to the '|detected 1>'-state of the detector, the qubit is in the state |1>, and relative to the '|detected 0>' state of the detector, it's in the state |0>. We think about this as moving from a superposition to a definite state, but this is really thinking as if we could hold the state of the detector fixed---but thinking about this as a relation between the detector and the qubit, the three propositions 'relative to |ready>, the qubit is |0> + |1>', 'relative to |detected 1>, the qubit is |1>', and 'relative to |detected 0>, the qubit is |0>'---which are not actually in conflict at all, and hence, can well be part of a consistent structure.
As for my 'middle way' between the naive box-of-things view of the world, and the---to my way of thinking---somewhat too rarefied view of relata-less relations, I don't really go into that in the present essay, but the germ of the idea---which is still pretty much all I've got---is in my entry into last year's contest, where I essentially propose that there are fundamental facts only relative to a certain perspective on the world, or a certain way to split the world into distinct subsets, or sub-objects, or perhaps, subject and object. It's a bit of a tightrope walk, and I'm far from certain something like that can be made to work at all, but not really liking to drop to either side, it's kinda all I got.
I hope you manage to meet all your deadlines!
Cheers
Jochen
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Jochen Szangolies replied on Apr. 26, 2020 @ 07:41 GMT
Dear Marcus,
I think the sort of explication of structure you're looking for might work along the lines developed by Lutz in '
Newman's Objection is Dead; Long Live Newman's Objection!'. Lutz essentially points out that there's no real way out of Newman's objection if the usual, Ramsey-sentence based notion of structure is used, but argues that this notion is insufficient anyway, and proposes to use an isomorphism-based notion: some sets A and B provided with relations R and S respectively have the same structure if and only if there is a one-to-one relation between A and B such that for all elements a1 and a2 of A such that a1Ra2, they are mapped to elements b1 and b2 of B such that b1Sb2.
I haven't gone through the complete paper yet, but so far, it seems promising.
Cheers
Jochen
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Author Markus P Mueller replied on Apr. 27, 2020 @ 09:01 GMT
Dear Jochen,
the points that you are raising are very interesting, but going into quite far-reaching details so that I feel I really want to read your essay first (and last year's again) before commenting much further.
In a very brief nutshell, I've tried to lay out my view in detail in arXiv:1712.01826. It is in some sense much more radical. In a nutshell, I would say that the following two situations are absolutely ontological identical:
(1) We are parts of a physical universe in roughly the way that we intuitively believe.
(2) We are brains in a vet or a simulation, yielding exactly the same observations as in case (1).
My argument is that all that there is, in a way, is an observer's state, and some chance of what this state might be next (and the form of this is the unique primitive structural claim). There is not *one* world, or *many*, but *zero*. To a view of this form, many standard objections and problems don't apply. Instead, one then has to argue why it typically so looks to the observer *as if* they were part of some "world", with computation, "things" and intersubjectivity. That's what I'm claiming to do, in an abstract sense, in that paper.
Now, I don't jut want to spam the world with the details of my pet view, so let me not go much further into this, and instead read your essay and comment on it to continue our discussion.
Maybe a final comment for now: the "simulation" problem that you mention is discussed a lot in the context of algorithmic information theory. As an arbitrary example (that you may enjoy), here's a paper by Marcus Hutter: "A Complete Theory of Everything (will be subjective)". What's said there (and elsewhere) is that it's not enough to have a theory that contains what you see (otherwise: dovetail all computable universes, done!), but you have to say where you are in it (observer localization).
Best,
Markus
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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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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
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
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
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
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
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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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 define physical reality.
You note that Special Relativity tells us that we cannot answer whether two events are simultaneous. Is this the end of the story? Or should we, as the Theorem and final paragraph in Section II suggest, take this unanswerable question as a deep insight into the possible existence of distinct differentiations?
Special Relativity assumes that all inertial reference frames are equally valid. This is empirically consistent with SR, but it is an added assumption about the nature of physical reality. It leads to 4D spacetime and no definition of simultaneity. Klingman’s essay describes an alternative reality, based on a contrarian assumption that physical reality is contextually defined with respect to a particular inertial reference frame. This structure/conceptual model is also empirically consistent with special relativity, including time dilation, but it describes a 3D space with a single time frame, and it embraces simultaneity.
In my essay, I describe the Copenhagen Interpretation as an empirical model of QM. It is focused on predicting measurement results and explicitly avoids questions of underlying reality. As such it is an undifferentiated theory, in which the question “Is randomness fundamental?” is unanswerable.
I consider more-differentiated structures to describe contrasting conceptual models of quantum reality. One conceptual model (I call HCM) adds an assumption that denies fundamental randomness. This assumption equates the wavefunction with physical reality, and both are fundamentally deterministic. I also describe an alternative model, which I refer to as DDCM. It recognizes that absolute zero can be approached but never attained, and it assumes that physical reality is contextually defined with respect to a positive ambient temperature. It describes physical reality as fundamentally random and irreversible. Both structures are empirically consistent with QM, but they yield contrasting answers to the questions of fundamental randomness and irreversibility. (DDCM also resolves the measurement problem and other conceptual difficulties of QM.)
I suggest that the metaphysics of “things” corresponds to a context-free physical reality. Things have independent existence. The metaphysics of structure, which “manifests itself by, and weaves together, ‘real patterns’” corresponds to a contextual physical reality, in which elements of reality are defined by their relationship to their objective physical context. Contextual reality with respect to a positive ambient temperature provides a firm foundation for your final hypothesis of a fundamentally probabilistic quantum reality.
I hope you will take a look at my essay and provide your thoughts.
Sincerely,
Harrison Crecraft
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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
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
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
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
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
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
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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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 since Aristotle, individual objects with determinable intrinsic properties) as an "epistomological obstacle" as philosopher Gaston Bachelard might say. A metaphysical distancing from the notion of “things”. While I was preparing my essay, I came across this quote from Rothstein, which I think might be in line with your “dissolution of questions” : an `` operational meaning can be assigned to question with respect to a system of interest which does not include the observer. Applied to the universe as a whole, these question lose their operational significance and become physically undecidable, they become metaphysical questions.''
I really enjoyed your defense of an “optimistic” view. It is true that interpretations acknowledging this analysis are very often mistaken with “incomplete” knowledge (epistemic restrictions) about ontic things ; or they are straightforwardly labelled as anti-realistic, without specifying “anti-realistic towards what”. Not towards the existence of an external word, but towards the notion of “things”.
I guess there might an ambiguity in your essay (or a misunderstanding from me), because I don’t see QBism as “an epistemic restriction” which can be compared with Spekkens’s view. I rather see it as something that might get along with your view, an optimistic position based on acknowledging that some “questions don’t have answers” not because of a lack of human ability, but based on a fundamental, logical argument.
Instead of taking a metaphysical stance as you do, arguing for an ontological realism of structures ; I tend to be sceptical towards sentences such as “the world is” (which are often related to a naïve realism (based on “things”)). So I am not sure that I completely rely on your view that “the world is about structure”. The word “structure” seems quite vague and ambiguous… and I prefer (for now) to strive for an “epistemological modesty” rather than designating what is ontological or not. However, you solution is way more appealing than naïve realism, since it is proposed after a careful analysis about the (un)decidability of questions. So I rather prefer your conclusion : “We can know what there is to know.” Which resonate with Bohr-like sentences : “There is no quantum world. Physics is about what we can say about nature”.
If you ever find the time to read my essay, I would be glad to have your feedbacks on it. You go further than my analysis, proposing an ontological path to follow (structuralism) while I stopped at the dissolution step (for now). However, your notion of “Structural differentiation” seems rather close to my concept of “meta-contextuality”, and I am very curious to have your thoughts on this.
I hope that your essay will do great in the contest.
Best,
Hippolyte
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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
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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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 is the question here then how our discrete observational experience of a 3D world emerges from the probabilistic structure of our observations? 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? A sort of QBist realism meets radical empiricism for which there is only the real patterns of our observational experience?
I’ve long been a fan of Dennett’s take on phenomenal experience (the manifest image) and its ‘real patterns’, or the persistent regularities of our sensory perception (cf. Husserl). Our species has evolved to perceive complex patterns in the phenomenal flux of visual, auditory, chemical, and somatic sensory experience, and where those patterns are predictive they can be considered ‘real’, with the natural (phenomenal) numbers being a case in point. I take it Peano’s axioms would then be an account of the modern structural relations evident in the real patterns of our natural/phenomenal counting experiences, along with whatever ontological assumptions that might motivate those axioms? Such as, for some, a rather quaint (and in this case a posteriori) belief in Platonic realism for numbers.
The ontic/conceptual structure then consists of identifying the dynamic relations between factical/real patterns—with structure defined by ontological and mathematical concepts that can explicate those patterns in terms of formalized predictions—and the history of science becomes the history of technological advances in our real pattern finding (from Kepler’s telescope to the Michelson-Morley experiment and on to Aspects’ entangled photons) leading to whatever necessary paradigmatic updates might be needed on the structural relations side with their subsequent technological innovations and so on… Which brings us to the contemporary conceptual mess of 21st C quantum foundations!
In this way the structural ‘laws of physics’ and the ontology that informs them emerge from the real patterns observed in scientific/empirical experience. So your ontic structural realism is then an observer dependent realism? I assume this is where your 'law without law' research project begins, with a first person perspective using algorithmic probability to assign structure to sense data patterns? What is real are the patterns (the information) … where an observer might be defined as nothing more or less than the flux of its observations situated, by simple definition, at the centre of its observable universe of real patterns and their probabilistic structural relations.
And finally, is it this first person ontology of the observer that might provide a structural differentiation from the early modern (delusional) godlike third person perspective that reduces the observer to a simple automaton located in an unobservable classical container world of the Ding an sich?
Apologies for crowding your thread but I find these questions fascinating and closely aligned with my own philosophical prejudices!
All the best,
Malcolm
Je suis, nous sommes Wigner!
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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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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 managed to formulate what I mean so clearly, even clearer than I did myself in the essay!
Regarding Dennett’s real patterns, I’m a big fan of this (and referencing it myself), but I think there is a hidden subtlety that is related to other issues like Goodman’s New Riddle of Induction. 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 really like this paragraph of yours:
“… and the history of science becomes the history of technological advances in our real pattern finding (from Kepler’s telescope to the Michelson-Morley experiment and on to Aspects’ entangled photons) leading to whatever necessary paradigmatic updates might be needed on the structural relations side with their subsequent technological innovations and so on… Which brings us to the contemporary conceptual mess of 21st C quantum foundations!”
:-)
Very well described!
Just a final comment on this question of yours:
“I assume this is where your 'law without law' research project begins, with a first person perspective using algorithmic probability to assign structure to sense data patterns?”
Even though algorithmic probability is used in this approach, the idea is somewhat different. In some sense, it starts with a form of methodological solipsism: there is your state S now (intuitively, containing your sense data and memory), and you will be in another state T next. In that approach, what that next state will be doesn’t depend an any “external world” (as we would usually think), but only on algorithmic probability P(T | S). Why such an approach? Well, suppose we are interested in “observer paradoxes” like Parfit’s teletransportation paradox (or others, e.g. simulating observers on a computer), and we claim that there is an objective chance of what such an observer will see in those situations. Then the answer, almost by definition, cannot be grounded on properties of the external world (even if there is one).
Surprisingly, one can show that, if we assume such law, then things look in the long run, for any observer, pretty much *as if there was* an external world. So the notion of “world” is emergent there, and an abstract notion of “self” is fundamental.
In case you’re really interested, there’s a link to an online talk on my homepage (mpmueller.net). But enough of advertisement.
I’ll try to have a look at your essay. I’m curious now!
Thanks again, and all the best,
Markus
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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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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 what predicates/basic concepts you might use as a basis for the construction of different sorts of compression algorithms for resolving simplified but predictive patterns from complex data sets … I’m just not sure that an ultimate definition of a ‘real pattern’ can be derived from that algorithmic perspective.
Could it be the case that an ontological (natural language) definition of a ‘real pattern’ derived from one’s own observational experience is precisely what you would need as a basic concept for the construction of algorithms that might then more or less model that observational reality? But if you already define a ‘real pattern’ as something that’s derived from a background of raw data vs noise, then your ontology is already Quinean at best, and at worst an externalist realism of mere pattern appearances weakly emerging from the external data/noise background. Thus a definition of a ‘real pattern' is derived from the ‘data’ (patterns)…
From a phenomenal (empirical) perspective, we don’t observe raw data and noise but rather we observe the patterns that we call ‘raw data’ and ‘noise’ … pattern recognition as the basic form of phenomenal experience is in this sense a priori, and the concepts of data and its inverse in noise, are both derived from that basis. What else is structural realism than intuiting structure within real patterns, where there is nothing beyond or behind the real patterns themselves?
And is a definition of ‘reality’ then nothing more or less than the degree of correlation observed between different algorithmic pattern recognition systems? Non-correlated systems would be orthogonal systems incapable of the communication of any recognisable pattern, whereas ‘we’ obviously already exist in a world of observable and very concrete pattern correlations. At least, that's how I understand a perspectival (intersubjective), observer dependent reality.
Cheers,
Malcolm
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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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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 discussion with you and your friends...
Meanwhile he asked me about my possible fundamental concepts??
These are the Fundamental concepts of Dynamic Universe Model taken from my essay, Have a look at my essay for further details....C.1. Logical and Physical foundational points of Dynamic Universe Model:
-No Isotropy
-No Homogeneity
-No Space-time continuum
-Non-uniform density of matter, universe is lumpy
-No singularities
-No collisions between bodies
-No blackholes
-No warm holes
-No Bigbang
-No repulsion between distant Galaxies
-Non-empty Universe
-No imaginary or negative time axis
-No imaginary X, Y, Z axes
-No differential and Integral Equations mathematically
-No General Relativity and Model does not reduce to GR on any condition
-No Creation of matter like Bigbang or steady-state models
-No many mini Bigbangs
-No Missing Mass / Dark matter
-No Dark energy
-No Bigbang generated CMB detected
-No Multi-verses
C.2. Main ETHICAL foundational principles of Dynamic Universe Model:
-Human Accrued knowledge should be free to all
-Concept should come out from the depth of truth;
-Authors / Scientists thinking should go towards perfection;
-Logic should be simple
-Theory’s predictions should be verifiable experimentally, by anyone and anywhere with the same conditions
-Computations / computer programs should be simple
-ontological realism of senses produced information
-New theory lead us forward into ever-widening thought and action experiments
-Let the new theory lead us into that heaven of freedom.
C.3. Main PHYSICAL and COSMOLOGICAL foundational principles of “N-Body problem solution: Dynamic Universe Model”:
-Natural universe regularly undergoes change in shape due to mutual Dynamical
Gravitational forces.
-Accelerating Expanding universe with 33% Blue shifted Galaxies
-Newton’s Gravitation law works everywhere in the same way
-All bodies dynamically moving
-All bodies move in dynamic Equilibrium
-Closed universe model no light or bodies will go away from universe
-Single Universe no baby universes
-Time is linear as observed on earth, moving forward only
-Independent x,y,z coordinate axes and Time axis no interdependencies between axes..
-UGF (Universal Gravitational Force) calculated on every point-mass
-Tensors (Linear) used for giving UNIQUE solutions for each time step
-Uses everyday physics as achievable by engineering
-21000 linear equations are used in an Excel sheet
-Computerized calculations uses 16 decimal digit accuracy
-Data mining and data warehousing techniques are used for data extraction from large amounts of data.
Best wishes to your essay
=snp
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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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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 structure.”
….. but only partly, because “undifferentiation of structure” acknowledges our persistence ignorance. In fact, that is point of my essay.
Please, make time to read my essay and grade it.
“Complete Information Retrieval: A Fundamental Challenge”
https://fqxi.org/community/forum/topic/3565
The universe is fundamentally stochastic because the observable radiations and particles are emergent oscillations/vibrations of the universal cosmic space, which is, at the same time, full of random “background” fluctuations. These fluctuations, however weak they may be, nonetheless are perturbing any and all other interactions going on in the universe. Since, human initiated measurements are also interactions between our chosen interactants in our apparatus, stochastical changes will be inevitable in every measurements, classical or quantum.
I am an experimentalist. Aprreciating persistent & continued incompleteness in our knowledge does not require complex philosophical arguments. Our measurements will always be imprecise. That we had been, we now are, and we will always be, information limited, emerges naturally when we enumerate the basic steps in any measurement:
(i) Data are some physical transformation taking place inside the apparatus.
(ii) The physical transformation in a detectable material always require some energy exchange between the interactants, the “unknown” and the “known”, where the “known” is the reference interactant.
(iii) The energy exchange must be guided by some force of interaction operating between the chosen interactants.
(iv) Since we have started with an unknown universe, from the standpoint of building physics theories, the “known” entities are known only partially, never completely. This also creates information bottleneck for the “unknown” entity. Note that in spite of innumerable experiments, we still do not know what electrons and photons really are.
(v) All forces of interactions are distance dependent. Hence, the interactants must be placed within the range of each other’s mutual influence (force-field). Force-field creates the necessary physical “entanglement” between interacting entities for the energy transfer to proceed. In other words, interactants must be “locally or regional” within their physical sphere of influence. They must be “entangled” by a perceptible physical force. Our equations are built on such hard causality.
(vi) The final data in all instruments suffer from the lack of 100% fidelity. This is another permanent problem of imprecision. We can keep on reducing the error margin as our technology enhances; but we do not know how to completely eliminate this error.
Many of my earlier papers have also articulated this position. They can be downloaded from:
http://www.natureoflight.org/CP/
You can also download the paper: “Next Frontier in Physics—Space as a Complex Tension Field”; Journal of Modern Physics, 2012, 3, 1357-1368 , http://dx.doi.org/10.4236/However, mp.2012.310173
Sincerely,
Chandra.
Prof. ChandraSekhar Roychoudhuri
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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
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
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
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
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 scaleand 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
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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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 [space-time emerges subsequently, from this Hilbert space, after spontaneous localisation]. So, whereas Alice and Bob are two space-like separated observers from the viewpoint of a conventional Minkowski spacetime, who are making their respective measurements, the picture of the same set-up is very different in matrix dynamics. From the viewpont of this new dynamics, a correlated pair of say electron and positron in an entangled state are represented by operators evolving with time, but this evolution does not imply that the electron and positron are moving away from each other. We must not think of them as spatially separated. Also, one talks of simultaneity in Connes time, which plays the role of an absolute [reversible] time. When Alice makes a measurement on the electron, it simultaneously changes the state of the positron [simultaneous in Connes time]. But no travel or signalling is involved.
I explain this in some detail in this paper:
https://arxiv.org/abs/1903.05402
starting at the bottom of p. 26. Basically, there are two different ways of lookimg at an EPR event. One is the space-time-less matrix dynamics way [non-local but no signalling], and the conventional way..involves signalling. Quantum non-locality appears to violate relativity if we accept that QM needs space-time. But qm does not need spacetime - in fact spacetime is external to qm and must be removed so as to find a better description of qm. The matrix dynamics achieves that - because there is an absolute time, but no light-cones. Lorentz invariance is emergent.
I will be very happy to discuss this point further with you. Do let me know what you think.
Thanks,
Tejinder
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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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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 mind was not quite this formal: I was thinking of typical situations in which we have a natural, canonical choice of coordinate system -- for example, physicists on Earth, separated by 1km or so, performing a Bell experiment in which they agree to measure at the same time.
Now, to what extent is it fair to compare the case of quantum mechanics and the case of `the same time'? I acknowledge that this is up for debate. I take it that the difference that you point to is of the following kind: there *are* situations within QM in which we might want to speak of "the world being in some well-defined configuration" (at least relative to a certain interpretation of QM), for example, in cases where its state is in some kind of eigenstate or product state relative to a classically meaningful basis, perhaps. So "being in a well-defined configuration" isn't in itself necessarily meaningless (relative to certain interpretations of QM), whereas "happening at the same time" in GR is.
But despite this difference, there is also a similarity that, to me, seems more compelling: the fact that the world, *in some cases*, *cannot* be regarded as being in some actual configuration is an important structural element of the theory with strong predictive (or explanatory) power. I've tried to illustrate this with the example of device-independent cryptography: if the world is in no configuration, then it is impossible to spy on this configuration. I see this similarly as relativity of simultaneity, which is an important structural element of SR with strong explanatory power (though one would typically not name this principle, but "Lorentz invariance" as the workhorse of explanations).
Best,
Markus
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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
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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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. It started with these words, “The world we live in is well-described by quantum mechanics. What should we make of that? In a way, the answer to this question was once less positive than it is today. For although quantum theory is a tool of unprecedented accuracy … the intellectual lesson we have come to
derive from it has been one … of limitations. The best place to see this attitude is in a standard presentation of the Heisenberg uncertainty relations. It is almost as if the world were holding something back that we really had every right to possess: The task of physics, or so it was believed, is simply to sober up to this and make the best of it. … In contrast to this … the last ten years have seen the start of a significantly more positive, almost intoxicating, attitude about the basic role of quantum mechanics. This is evidenced no more clearly than [with quantum information and computing]. The point of departure in these disciplines is not to ask what limits quantum mechanics places upon us, but instead what novel, productive things we can do in the quantum world that we could not have done otherwise. In what ways can we say that the quantum world is fantastically better than the classical world?” Your paper brought back to me the romance of those lost days, but you did it so much better!
I had never previously thought about Goedel’s incompleteness theorem in the positive way that you do, even though some other writers should have led me close to it. When I read your words on that point, I immediately thought, that’s got to be right! “It is not a fundamental limit to what we can know, but a precious piece of knowledge about a non-property of the structure that we have discovered”—Beautiful!
Incidentally, in this paper of mine,
https://arxiv.org/pdf/1601.04360.pdf
I transcribed an entry from one of John Wheeler’s notebooks that blew me away when I first ran across it. I don’t think it’s exactly what you have in mind, but here’s the little story I wrote when introducing it: “Despite the dubious connection to anything firmly a part of QBism, I report Wheeler's idea because it seems to me that it conveys some imaginative sense of how the notion of ‘birth’ described here carries a very different flavor from the ‘intrinsic randomness’ that [Adan Cabello] and others seem to be talking about. … Imagine along with Wheeler that the universe can somehow be identified with a formal mathematical system, with the universe's life somehow captured by all the decidable propositions within the system. Wheeler's ‘crazy’ idea seems to be this. Every time an act of observer-participancy occurs (every time a quantum measurement occurs), one of the undecidable propositions consistent with the system is upgraded to the status of a new axiom with truth value either TRUE or FALSE. In this way, the life of the universe as a whole takes on a deeply new character with the outcome of each quantum measurement. The ‘intrinsic randomness’ dictated by quantum theory is not so much like the flicker of a firefly in the fabric of night, but a rearrangement of the whole meaning of the universe.”
You caused other thoughts in me as well. In the paper linked to above, I emphasized in a small piece of it that QBism shares *some* of its elements with a structural realism. But most philosophers of science I’ve told this to have been (predictably) dismissive. It’s hard to say what stands in their way, except possibly that if an idea is associated with QBism, it’s got to be bad! Upon reading you, however, I got a vision on how I might break the impasse: Make up a new name, a new distinction! Thus, from here out I will dub QBism’s distinctive flavor “normative structural realism.” But I will discuss this with you offline sometime.
In any case, I write all of this to let you know, in my eyes your essay has everything that should be expected of a winner of this contest. I learned a number of things from you, but mostly your essay caused me to think over and over about its contents all week. It hasn’t left my mind, and that’s a mark of distinction in an old doddering mind like mine!
All the best,
Chris Fuchs
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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 scaleBut 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
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
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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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 different in the different subtheories). That certainly sounds right to me! How prevalent is this way of thinking about the incompleteness theorem? I haven’t studied the literature on incompleteness, so I have no sense of whether or not this is “conventional wisdom” in some circles. Hofstadter, at least, does characterize the theorem in this manner in Godel, Escher, Bach (among the many ways that he characterizes it). Similarly, it seems to me that Chaitin does so as well. Did Godel think of it in this way?
In any case, very nice essay! I enjoyed it a lot.
A minor point. When you get to the analysis of quantum theory, you contrast your own view with the view that quantum states are states of knowledge about some kind of hidden variables. You call the latter “Spekkens-like interpretations”. Presumably, that’s because I’ve written many papers about subtheories of quantum theory and foils to quantum theory (such as my toy theory) that admit of such an interpretation. But the terminology makes me uneasy insofar as it may suggest to some that I endorse the view that such an interpretation might be possible *for the whole of quantum theory*, which I certainly do not. A better name for this type of interpretation of quantum theory would be “psi-epistemic hidden variable models”. There are certainly some researchers who have made proposals of this type, but I am not enthusiastic about the research program because all such proposals have the same deficiencies as psi-ontic hidden variable models insofar as they necessarily fail to offer satisfactory causal explanations of quantum correlations. To grant that there are hidden variables to be discovered is to buy into the framework of ontological models, and I’m of the opinion that the correct interpretation of quantum theory must reject that framework. It seems to me that we need to pursue a rather different sort of realism, which is more “structural”, exactly in the sense in which you use the term in your article (i.e., in the sense of “ontic structural realism”). In particular, I’m fond of the idea that the structure of causal relations might somehow capture everything about reality, without there being causal relata in the form of classical hidden variables (this idea was described in an FQXI essay I wrote a few years back). It seems to me that a denial of this kind of causal relata might in fact constitute a denial of the possibility of answering a question such as “what is the actual configuration of the world?” If so, then our views are not so different, at least in terms of the status of this sort of question.
I am reminded of my favourite quote by the pragmatist John Dewey: "The conviction persists, though history shows it be a hallucination, that all the questions that the human mind has asked are questions that can be answered in terms of the alternatives that the questions themselves present. But in fact, intellectual progress usually occurs through sheer abandonment of questions together with both of the alternatives they assume, an abandonment that results from their decreasing vitalism and a change of urgent interest. We do not solve them, we get over them."
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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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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 2).
Indeed, I agree that our views on that particular question are not that different in some respects (different version of ontic structural realism in some sense perhaps), in particular compared to alternative views of some philosophers.
I am thrilled by your quote of John Dewey! It fits so well in many respects what I believe in, and what I have tried to convey in the essay. In retrospect, I do remember that you have mentioned this quotation to me before -- perhaps even in a talk of yours that I’ve attended. I'll dig up the reference to learn more about the context in which it was phrased.
Now, regarding your question — an interesting question indeed! I have no idea about Gödel’s or Chaitin’s intuitive or interpretational views on the incompleteness theorem; it would be very interesting to read up on this.
The mere technical statement — if there is a proposition such that neither itself not its negation can be proven, then one can add either one of the two as a new axiom — is of course very well-known. But what I am describing is not so much about this technical statement itself, but about what I think we can learn from it.
Take the natural numbers, N, for example. The conventional interpretation of the incompleteness theorem is as follows. Whatever axiomatic system we use (say, Peano arithmetic), there are always true statements about N that are unprovable within the system. Hence “the truths about N” can somehow not be “fully captured” within any axiomatic system.
This view implicitly claims that there exists this thing called N, fully differentiated, and somehow clear to us humans what it should be. It is as if we have encountered N in our mathematical backyard — here it is! — and now we just have to manufacture a good axiomatic system to formalize it.
But my view denies this. It sees mathematics as consisting of *structure* in the way that I have tried to describe in my essay: (necessarily undifferentiated) “things” that consistent theories talk about. In this sense, N itself is a fiction. Instead, there are many “N-like” structures that have more or less of the properties that we intuitively associate with the natural numbers.
Now, how widespread is this view?
Honestly, I have no idea. I agree that Hofstadter is gesturing at this view in some places, but as far as I remember from reading GEB, it is not discussed explicitly. Perhaps it *is* conventional wisdom in some circles, but then these circles do not seem to make much noise. :-) I’d really like to find out.
All the best,
Markus
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Sue Lingo wrote on Oct. 4, 2020 @ 07:02 GMT
Congratulations Markus...
In that your essay focuses attention on the necessity for one's choice of a Space-Time Energy "theoretical structure" to be associated with Space, as a precisely defined and specified "Geometric Structure", it is pivotal, and I can concur with FQXi's acknowledgement of its significance.
"Geometric Structures" as 3D CAD environments, in which geometry...
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Congratulations Markus...
In that your essay focuses attention on the necessity for one's choice of a Space-Time Energy "theoretical structure" to be associated with Space, as a precisely defined and specified "Geometric Structure", it is pivotal, and I can concur with FQXi's acknowledgement of its significance.
"Geometric Structures" as 3D CAD environments, in which geometry specific fundamental Q-mechanical functions... e.g. emission and distribution mechanix... can be digitally simulated (CAD SIMs), augment visual verification of fundamental foundations, to facilitate precise definitions of semantic terminologies that become embedded in subsequent "theoretical structures".
REF:
Directionally Unbiased Point Source Emission Mechanix www.uqsmatrixmechanix.com/UQST-TVNH.php
Is a minimum/indivisible quantum of Potential for Motion a "thing"?
A quantum Point Source Emission "theoretical structure", which is inclusive of Physics and Meta-Physics, is potentially viable, but one must first make a distinction between the term Physical and the term Meta-Physical.
To make a distinction between Physical and Meta-Physical, requires a precise definition of Physical that facilitates its identity as a subset within a larger set that is inclusive of other than Physical.
PHYSICAL entities are uniquely defined in terms of what?... spatial occupancy??
If one defines PHYSICAL "things" as discrete entities having spatial occupancy, one will need to define Space as a "Geometric Structure"... i.e. preferably as a 3D quantized CAD spatial environment... that facilitates an emission and subsequent spatial occupancy distribution of Physical entities, which is consistent with observation... i.e. recognizable "patterns" of spatially quantized Potential for Motion emerge.
A minimum/indivisible pulse duration... i.e. a Q-Tick...is required to facilitate a Timeless Intermittent Calculation State (ICS) in which to repeatedly resolve spontaneous, harmonious, directionally unbiased emission and subsequent spatial occupancy distribution, of all pulsed Single Point Sourced discrete minimum/indivisible units of spatially addressable Potential for Motion... i.e. emission and subsequent spatial distribution of pulsed, spatially discrete Energy quanta (QE)... within the entire field.
To digitally SIMulate emission pulse sourced motion, as CAD environment, x,y,z discrete Physical entity location incrimination, in a theoretical, temporally minimum/indivisible duration, one needs to define the SIM frame rate as the emergent Physical entity emission pulse count... i.e. pulse count as the minimum/indivisible quanta of discrete Time (QT)... and doing so, implies that a perception of time is spatially dependent.
If Meta-Physical is differentiated from Physical by means of a spatial occupancy criteria, then Meta-Physical operatives require a Spaceless Logic Structure.
Does a feeling of spatial occupancy, occupy Space?
To define META-PHYSICAL as other than that which occupies Space-Time, a dimensionless logic environment in which Spaceless-Timeless operatives/mechanix... e.g. a feeling.... are consistent with observation, is required to coherently integrate Physics and Meta-Physics in a quantum "theoretical structure".
From a Space-Time Geometry Singularity... i.e.. a 3D "geometric structure" which encapsulates a single dimensionless point... the root architecture for an intelligent network... i.e. Cosmic Consciousness... emerges as the logic codec between the Spaceless-Timeless Logic framework and the Space-Time Logic framework, and given a logic codec integration of these two discrete logic evaluation frameworks, the ability for Meta-Physical operatives to resolve Physical entity emission mechanix, and for Physical entities to influence Meta-Physical operatives, are potential fundamental mechanisms, and justify investigation.
In which logic framework is Space-Time Energy quanta (QE) distribution resolved by Laplace's demon?
If from a Spaceless-Timeless logic framework, Laplace's demon could "feel" the QE occupancy of each individual minimum/indivisible unit of discrete Space (QI), within the entire field... i.e. "know" Space-Time as a Spaceless feeling of Timeless now... and utilize the Spaceless-Timeless/Space-Time codec... i.e. cosmic intelligence,.. to spontaneously, harmoniously resolve the QE/QI re-configuration for the entire field, within each pulse interval of one timeless Q-tick.
If a CAD modeled "geometric structure" in which QE emission and distribution SIMs verify a fundamental PROCESS that resolves spontaneous, harmonious QE/QI occupancy for the entire field, on each Q-Tick, and facilitates a codec for Space-Time entities to query cosmic intelligence at any Time "now", is installed as an upgrade to prior concepts of Demon, and/or God ENTITIES, a structural change in human consciousness is facilitated.
Can one "know" the QE occupancy configuration of the entire QI space-Time Energy field on any Q-Tick?
If the analysis structure constrains one's query, a "question without an answer" does NOT dissolve the question, and although Physical limits on current CAD SIM computability restrict the field frame, the "geometric structure" and initial state emission mechanix are verifiable within those constraints... i.e. available QI address path dictates and valid mechanix to facilitate unprecedented solution reduction in Quantum Energy (QE) analysis within any subsequent purturbative... i.e. without verifiable unbroken kinematic logic chain to the Point Source Singularity... frame of the QE/QI field, can be inferred.
One can not dismiss the possibility to "know" the individual QE/QI occupancy configuration for the entire field, on any QT, without first eliminating any possibility of resolving a CAD "geometric structure" in which QE emission and subsequent distribution SIMs verify spontaneous, harmonious QE/QI resolve on each QT, and the impossibility of knowing whether that is possible, can only be dissolved by doing so.
Geometry analysis of fundamental motion mechanix, without resolve of a Geometry Singularity... i.e. point source encapsulation... is inherently purturbative.
Fundamental PROCESS resolved QE/QI choreographies/patterns, as logic circuits which are infinitely scalable within the field... e.g. humans... that purturbatively monitor and data process Space-Time Energy observations are unable to verify a cosmic intelligence, and with regard to a fundamental PROCESS, are tolerating "Undecideablity, Unpredictability, and Uncomputability".
Given a causality model that is neither deterministic nor random... i.e. one in which on every pulse, the QE/QI configuration of the entire system must be resolved on the basis of internal agent/circuit monitoring... if the functionality of the monitoring circuit is inhibited by "Undecideablity, Unpredictability, and Uncomputability", the agent/circuit will experience confusion, and may induce local disharmony.
"Can one "know" if event A and event B are simultaneous?"
Not if one's analysis is constrained to a rubber sheet "geometric structure" in which Space and Time are continuous, and Energy is a numerical representation of a qualitative physical property measurement... e.g. heat... associated with an observable event in which neither Space nor Time is discrete... i.e. Energy is NOT a spatially defined entity.
As inferred by E=mc^2, PHEnomenal Energy (PHE) as an accelerated Mass observation quantifier, does NOT facilitate an analysis of an "event" as motion, in terms of CAD environment x,y,z location incrimination of a minimum/indivisible spatially defined entity, within a theoretical minimum/indivisible temporal duration... i.e. PHEnomenal Energy (PHE) must be differentiated from spatially discrete Energy (QE) in a quantum model.
A visual comparative of two temporally sequential snapshots, of discrete QE occupancy within discrete QI, is required to verify motion A and motion B are simultaneous... i.e. both occur within 1 Q-Tick.
If one utilizes a "geometric structure" in which static Space is quantized by QI, Time is measured in Q-Ticks (QT), and Potential for Motion is spontaneously, harmoniously distributed as continuously pulse sourced QE... i.e. Space, Time, and Energy are discrete elements of the model... simultaneous QE motion events are inherent.
To "know" that a motion event experienced by spatial entity A, and a motion event experienced by spatial entity B, are simultaneous, is facilitated by a visual comparison of two sequential freeze frames... i.e. 1 Q-Tick... of the emission SIM.
Utilization of "statistical patterns" as a semantic unifier to achieve "integration of both views"... i.e. probabilistic entanglement and discrete functionality... evades the necessity to acknowledge observations of Meta-Physical operatives influencing Physical entities, and vice versa.
As currently practiced... i.e. without verification of an unbroken kinematic logic chain to the Point Source Singularity... FUNDAMENTAL investigation by means of statistical analysis, escalate "Undecideablity, Unpredictability, and Uncomputability", inducing a credibility barrier, and inhibit utilization of observable Meta-Physical operatives to resolve inability to "know".
I have repeatedly recorded an experiment that verifies the outcome of a flip of a coin is influenced by a sufficiently enhanced QE choreographed logic agent's/circuit's... e.g. human's... binary query of the cosmic intelligence, which suggest that the root architecture of the cosmic intelligence, as the network element of the PROCESS, allows Physical entities and Meta-Physical operatives to interact, and a valid FUNDAMENTAL PROCSES model must facilitate this exchange functionality.
In that a demonstrable CAD SIM resolve of spontaneous, harmonious, directionally unbiased emission and subsequent spatial occupancy distribution, of pulsed Single Point Sourced discrete minimum/indivisible units of spatially addressable Potential for Motion, promotes creditability for Physical and Meta-Physical integration, and visually resolves fundamental mechanix which enable statistical analysis of FUNDAMENTAL PROCESSES as required to enhance human Physical and Meta-Physical design and functionality, thereby accelerating technological developments and applications, an upgrade from prior reliance on statistical purturbative analysis as a means to explore FUNDAMENTAL territory, is justifiable.
In that the dynamics and functionality of QE choreographies... i.e. Physical "patterns"... which emerge as a result of spontaneous, harmonious resolve of a pulsed emission and subsequent distribution of Potential for Motion, within addressable,... i.e. uniformly defined, static and discrete... minimum/indivisible spatial units (QI) of a quantized "geometric structure", are inherited from a FUNDAMENTAL PROCESS.. i.e. the initial state emission mechanix as dictated by the QI address path potential of the Point Source Singularity quantization... all dynamics and functionality of subsequent QE choreographies, postulated by "theoretical structures" must map to the quantization of the associated "geometric structure".
Given that "correct" implies Physical and Meta-Physical integration, "to discover the correct geometric structure", requires resolve of a Geometry Singularity quantization which as the root architecture of a networked intelligence, facilitates a codec... i.e. logic unification... between the Spaceless-Timeless and Space-Time logic structures, and resolves continuous emergence of dynamic "patterns"... i.e. QE choreographies... which are consistent with observations both Physical and Meta-Physical.
"3D physical bounded spaces in motion render 'space-time' and 'wire frame' Cartesian systems inadequate modeling tools. Yet we agree Minkowski; "Everywhere there is substance". (1906)." ~ 2019 FQXi Essay REF:TOPIC: Blondes, Brunettes & the Flaw of the Excluded Middle by Peter Jackson
Consensus with regard to a "hole" in a "theoretical structure" is difficult to obtain, and a "hole" in a "theoretical structure" does not necessarily imply a "hole" in an associated "geometric structure".
As a means to validate theoretically postulated immeasurable Physical elements, as elements within the "geometric structure", the ability to see broken kinematic logic chains as discontinuities in SIMulatied PROCESSES within the CAD "geometric structure", is pivotal.
The question "What are the properties of aether?", if analyzed within the constraints of a "geometric structure" in which Space is continuous, may have no answers, but if aether is the quantization geometry of the "geometric structure"... i.e. the intelligence element of all FUNDAMENTAL PROCESSES... aether properties can be associated with the uniform minimum/indivisible discrete quanta (QI) of fixed addressable spatial QE containment.
In that digital CAD SIMs analysis facilitate virtual visual verification of theoretically postulated immeasurable Physical elements, if as above, Physical is differentiated from Meta-Physical by a spatial occupancy criteria, ambiguities emerging from Meta-Physical entities and operative as indistinguishable from immeasurable Physical entities and operatives, is resolved.
"We can know what there is to be known.", but Physical limits do not infer a limit on what can be extracted as knowledge from an integration of Physical and Meta-Physical functions of "knowing", and therefor I can not agree that questions not yet solved, dissolve.
Sue Lingo
UQS Author/Logician
www.uqsmatrixmechanix.com
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Alec Misra wrote on Mar. 22, 2021 @ 05:21 GMT
Ha ha, I can tell this is sheer bullshit just by reading the abstract alone.
You write:
", I argue to replace this perspective by a worldview in which a structural notion of ‘real patterns’, not ‘things’ are regarded as fundamental"
Now, epistemically this is identical to saying:
", I argue to replace this perspective by a worldview in which "Jesus Christ is my saviour" should be regarded as fundamental."
And they give first prize to such nonsense? Its pathetic. Why dont people make way for people who actually know something about these subjects? That would be a radical change woukdnt it?
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Malcolm Riddoch replied on Mar. 28, 2021 @ 20:42 GMT
Hi Alec,
I’d be very interested to hear why you think an experimentalist commitment to a form of objective realism based on Dennett’s notion of ‘real patterns’—or notions of ontic structural realism, or wave function realism for that matter—is ‘epistemologically identical’ to a profession of faith in the gospels’ Yeshu.
I take it you place your faith in a metaphysics of ‘objective reality’ based on discrete things/particles in a classical spacetime as opposed to ... a faith based empirical belief in an information/theoretic ‘it from bit’ reality? Or somesuch?
I personally can’t see the religious connection, but then I’m a philosophical agnostic who also upvoted Mueller’s excellent essay on structural realism in quantum foundations.
Regards,
Malcolm Riddoch
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