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January 19, 2018

CATEGORY: FQXi Essay Contest - Spring, 2017 [back]
TOPIC: Four Verses from the Dàodéjīng by Jochen Szangolies [refresh]
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This essay's rating: Community = 7.1; Public = 9.0


Author Jochen Szangolies wrote on Jan. 9, 2018 @ 21:06 GMT
Essay Abstract

We engage the world via models. However, every model is necessarily incomplete: the faculty by which modeling works cannot itself be modeled, and thus, remains opaque to understanding. We thus apprehend the world with tools intrinsically incapable of encompassing it as a whole. I propose that several challenging philosophical problems are in fact expressions of this limitation. Among them is the problem of fundamentals: since every model of the world reduces to some set of fundamental facts, we expect the same thing to hold of the world as a whole. This, however, ultimately confuses the map with the territory.

Author Bio

Jochen Szangolies acquired a PhD in quantum information theory at the Heinrich-Heine-University in Düsseldorf. He has worked on quantum contextuality, quantum correlations and their detection, as well as the foundations of quantum mechanics. He is the author of "Testing Quantum Contextuality: The Problem of Compatibility".

Download Essay PDF File




Stefan Weckbach wrote on Jan. 10, 2018 @ 04:59 GMT
Hi Jochen, you took a rather constructive approach (not to say radically constructive) to tackle the essay contest’s question and you provide some interesting arguments.

Let me therefore make some probably helpfull, but also critical comments.

I conclude from your two propositions, when considered as true, that nature cannot possibly be exclusively only a deterministic system –...

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Author Jochen Szangolies replied on Jan. 10, 2018 @ 06:02 GMT
Hi Stefan,

thank you for your comments. Unfortunately, I don't have time to reply to them in full right now, but I think there's a potential misunderstanding here that I wanted to try and head off.

In a nutshell, my proposal is that the world, as such, is non-computational---indeed, I view computation ultimately as a subjective notion: a system computes only if it is interpreted as computing something. This isn't really different from other symbols (since ultimately, the states of a computing system are just symbols). A set of cracks in a rock made by natural processes a billion years ago, before any humans were around, has no meaning, even if it happens to spell out something (indeed, I remember the case of an alleged runestone turning out to be just such a natural phenomenon; nevertheless, a 'translation' of it had earlier been proposed).

However, our minds use symbols, and---if my two propositions are right---perform computations. For this to be possible, this computation must be underwritten by a process that is not itself computational---otherwise, we'd end up in an infinite regress. The hypothesis that it's qualia that underlie this mental computation then serves to ground it, and also explains why qualia are such a challenging concept---because we can't make computational sense of them. (Note that it doesn't mean qualia are all there is to consciousness.)

So, in brief, we use computational reason, modeling, to try and explain a noncomputational world---which is only ever possible partially. This is not such a radical proposition, really: it's the situation we've been in with respect to mathematics ever since the Gödelian incompleteness theorems. There, things are often phrased as if they're a problem for mathematics---'mathematics is incomplete', or something of that sort. But really, they're just a problem for mathematicians: because human mathematicians are limited to effective, formalizable means, no axiomatization we could come up with can encompass 'all of mathematics'.

If I'm not completely off-base, then the same thing holds of the physical world: no model ever encompasses it completely. Consequently, holding any particular model's base facts as 'fundamental' is just as misguided as thinking of any particular set of axioms (that are accessible to human mathematicians) as 'the axioms of mathematics'.

As for determinism, that's actually an interesting question I didn't have the space to engage in the essay. Basically, you can represent every noncomputable function as a computation augmented with a string of random numbers (see, e.g., here). Consequently, a computational reason, faced with a noncomputational world, could at best understand it as some deterministic evolution with interspersed random events---which is of course exactly what we actually have in quantum mechanics. So here, too, the hypothesis that we're trying to apprehend a noncomputational world with computational means seems to hold some intriguing explanatory potential.

To me, this seems then a fairly simple idea, with precedent in pure mathematics, that serves to elucidate many otherwise puzzling features of the world.

I'll try and get back to some of your more in-depth remarks and questions when I have more time.




Stefan Weckbach wrote on Jan. 10, 2018 @ 08:07 GMT
Hi Jochen, thanks for the almost immediate reply, which clarifies a lot for me about your approach.

It seemed to me by reading your essay that there is a huge contradiction in assuming that the ‘mysterious’ interface between Qualia and the external reality should not be computationally describable in principle, but nonetheless should work via a deterministically acting (turing-complete) mechanism.

This arose to me as a mystery par excellence, since it then would transform the mystery of Qualia itself into the mystery of how one can justify to having the cake (a turing-complete interface) and at the same time eat it (having Qualia and consciousness defined as being completely equivalent to to a turing-like computation).

Therefore I wrote that maybe it perhaps is the other way round ---- and asked myself why nobody can see the possibility that it is no wonder that Qualia isn’t computationally definable ----- because it may turn out that computations, at least deterministical ones, are not the only things that reasonably can exist.

You wrote that

“But really, they're just a problem for mathematicians: because human mathematicians are limited to effective, formalizable means, no axiomatization we could come up with can encompass 'all of mathematics'.”

Yes, I fully agree; and I would add that it is only a problem if one has a platonic view of mathematics and its axiomatization as an eternally fixed (infinite) set of (infinitely) complex relationships.

It would be interesting to me whether you define the process that underlies our mind’s capabilities to perform computations as ‘computations’ in the sense that they are augmented partially with a string of random numbers – for example for human decision processess.

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Author Jochen Szangolies replied on Jan. 10, 2018 @ 17:40 GMT
Hi Stefan, glad I could help some. You're right to say that it would be mysterious to first characterize qualia as noncomputational, and then turn around on a dime to claim a computational mind after all (if I understand you correctly and that is what you're saying), but that's not my intention---rather, it seems in some agreement with you, I think that qualia are noncomputational phenomena, and...

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Stefan Weckbach replied on Jan. 11, 2018 @ 08:57 GMT
Hi Jochen, thanks for your comments. Yes, that was my problem. As I understand it now, you define the underlying process of connecting the stuff in the world with our mental constructs as Qualia, the latter fundamentally irreducible by any analytical means. Is this the correct version of what you are proposing? Since the problem of infinite regress and Gödel’s incompleteness theorems can be regarded as two sides of the same coin (regarding self-reference), does your approach at present also involve the notion of mathematical infinities, the latter having anything to do with the fact that Qualia are at all possible to exist (as they obviously do) in the framework of your approach?

Meanwhile I have written a reply to your comment on my essay page. I have clarified some points you may have misunderstood about my own approach and gave a rather extensive story of why I concluded in my essay what I concluded and made some more statements on how to give it a precise meaning. As always, any questions about what I’ve written are welcome.

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Author Jochen Szangolies replied on Jan. 11, 2018 @ 18:08 GMT
Hi Stefan, yes, I think you've got the gist of my idea there. Qualia are mysterious, because they're not amenable to model-based reasoning; and they're not amenable to that because otherwise, we would end up in an infinite regress.

Regarding infinity, well, I'm skeptical of the physical implementability of anything actually infinite---after all, I consider something being only possible by traversing an infinite regress to be something that's actually impossible. Otherwise, I could just hold that well, you need an infinite number of computations to subserve modeling, so what?

But I think that doesn't mean that the notion of infinity doesn't have any value in thinking about the world. For one, there might be open-ended processes, which, while not infinite at any instant, nevertheless also can't be called finite. Furthermore, there are possibly things in the natural world that must seem infinitary to a computational reason. True randomness, for instance, cannot be produced by any finite computer program. But an infinite program could, in principle, produce a random real number (by the trivial method of storing infinitely many digits, for instance). So if the universe is an open-ended process, and quantum mechanics is truly random, then there is no finitary concept that suffices to capture it.

Regarding your reply on your essay page (which is almost another essay in itself), I probably won't get around to replying to that before the weekend, so I'm gonna have to ask for a little patience here...




Philip Gibbs wrote on Jan. 10, 2018 @ 17:29 GMT
Jochen, anthropologists are always trying to identify some "unique capacity" of humans that separate us from less evolved creatures, but the zoologists always spoil the idea. For example someone once claimed that humanity is an ability to make and use tools, but even animals such as birds and fish have been observed to use and even make simple forms of tools. I fear that our capacity for "constructing internal models of the world" may go the same way. Luckily this is a side issue that I think does not affect your main thesis.

Your essay has some ideas very much in tune with my own, but it also has some opposites which are possibly more interesting. You share a similar view to mine on the relation between nothing and everything in the context of information theory. Your response “Why this?” in answer to any proposal for fundamental theory also resonates well with me. Because of this I push back fundamentalism to a deep level using emergence, but whereas I still hold out hope for a system of mathematical meta-laws, you seem to go further and argue that there is no fundamental theory.

Your theory of models also seems to be opposite to mine. If we equate models with stories in my essay, then I argue that the real universe is the same as a model, whereas you argue that a model can never be the same as reality.

Do you see more similarities or differences? Whatever the answer, your essay is well argued and gives me a useful way to question my own view. I am glad you have been able to bring it under discussion with plenty of time left.

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Author Jochen Szangolies replied on Jan. 10, 2018 @ 17:59 GMT
You're completely right to question any claims of human uniqueness---and I don't want to claim that model-building is some uniquely human capacity (in fact, earlier versions of the essay contained many caveats regarding when in the evolutionary history of humankind this capacity first came up, but that ultimately didn't add much, as nothing really rides on the precise location of that point)....

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Philip Gibbs replied on Jan. 10, 2018 @ 21:22 GMT
Yes that does make sense. I also do get the point about our ability to reflect on ourselves. Even if I am skeptical about the phase transition and see it as a more gradual fuzzy change, the relevant part of the point is still valid. It is also meaningful in the context of my own essay.

Yes, our view of mathematics is incomplete because of undecidability and the formal systems we are limited to studying. There are models of mathematical logic which may be analogous to models of reality too. Somehow the universe must avoid the incompleteness that this potentially implies if physics is based on mathematics. You have a radical solution to problems like this through the noncomputability idea. The problem I see with this is that it seems to be saying something about what reality isn't, but it does not answer what it is. Are you saying that there is no answer to that?

I see things differently through a hypothetical principle of universality, but if that idea does not work I have to fall back on something like what you are saying. I'll say a little more about my view on my essay forum.

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Author Jochen Szangolies replied on Jan. 11, 2018 @ 06:06 GMT
You're right that my conclusion is essentially a negative one---again, this is like with Gödel's theorems: we won't find a single axiomatization of all of mathematics, it's simply too rich for that. Likewise, we can't tell a single story covering all of physics---reality is too multifaceted for that.

But that doesn't mean the end of science anymore than Gödel's results meant the end of...

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Georgina Woodward wrote on Jan. 10, 2018 @ 17:52 GMT
Hi Jochen, lots of interesting argument in your essay. I like your "Models are at the heart of our engagement with the world. When we think about a tree, there is no tree present in our thoughts; rather, we use a mental model in order to draw valid conclusions about the actual physical system." Though the conclusions are not always valid, they can be in error. Though sufficiently accurate, enough...

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Author Jochen Szangolies replied on Jan. 11, 2018 @ 17:58 GMT
Hi Georgina, thanks for your kind comments, I'm glad there was something for you in my essay.

Regarding the mirror test, I actually mostly tend to agree with you: it's certainly not necessary to be able to pass that test in order to have a sense of self, but I'm merely taking it the other way around---that having some idea of what 'you' are is necessary to pass the mirror test. Because by passing that test, a child, or ape, or bird essentially says 'that's me'; so there needs to be an idea of 'me' beforehand. I agree, though, that this isn't really clear from the way I put it in the essay.

So I think it's very well possible to have an internal experience of an 'I' without being able to pass the mirror test. Another example of such a situation might be with animals whose primary sense modality isn't vision. For instance, for a dog, vision just might not play enough of a role to take it into consideration enough to do all the data processing necessary to correlate the image in the mirror with itself; but a smell-o-vision version might be no problem (not that I know how that might look, exactly), while I could easily imagine humans failing such a test without our self-hood thereby being called into question.



Georgina Woodward replied on Jan. 11, 2018 @ 22:43 GMT
Thanks for your reply. Really good point about the different priority given to different kinds of sensory input by different species. I think it might be confusing for a dog to smell'itself' somewhere else, that it hasn't been and left its smell. I don't think I would recognize my own smell in isolation but imagine I would be able to eliminate not my smell of other people. And you are right we would not have the same kind of relation to the smell information as a dog. We would not identify that external stimulus with internal sense of self -causing the dog scientists to question our self awareness : )

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Brajesh Mishra wrote on Jan. 12, 2018 @ 15:55 GMT
Dear Jochen, I am impressed by your very methodical way of presentation and building of arguments / conclusions.

I cannot do but agree -->

The question “What is fundamental?” is already misguided: our instinct for searching for the fundamental is simply due to our model-based reasoning.

Best Wishes

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Author Jochen Szangolies replied on Jan. 14, 2018 @ 10:38 GMT
Dear Brajesh,

thank you for your kind comments. I'm very happy you found something that speaks to you in my essay!




austin fearnley wrote on Jan. 12, 2018 @ 21:46 GMT
I have written up my memories of thoughts as a two month old baby. See here in (2008) https://ben6993.wordpress.com/2008/09/13/early-memories-as-a
-baby/#comment-83

I wrote that "there must have been a change of phase at two months" so I agree with you about early phase changes.

I wrote my childhood essay as no one believes my memories are credible. One friend has childhood amnesia and cannot remember much under ten years old. Remembering under two years old is often deemed not credible.

I also wrote that "a fractal analogy is interesting. In fractals, a similar pattern is found on different scales. ... I was remembering different occasions of being awake (small scale – one day to the next – awake/asleep/awake/asleep etc.), but it seemed like different occurrences of life (large scale – one life to the next). Before the change of phase, prior awakenings seemed like prior lives as there was so little of ‘me’ to remember in them. And as soon as I was old enough to know that I was a continuing ‘me’, ie in the new phase, it was too late… as I had been deceived by the change of phase into remembering it as a prior “life” rather than just a re-awakening."

And maybe this sort of phase transition underlies [mistakenly ;) ] belief in reincarnation.

Despite all that striving to find my identity at two months, I would no doubt have failed the mirror test until much older than that.

The change of phase has nothing to do with my own contest essay, but my contest essay does look at fundamentality wrt quasi-fractal ideas so maybe my baby experiences pre-conditioned me to think quasi-fractals are generally relevant.

Best wishes

Austin

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Author Jochen Szangolies replied on Jan. 14, 2018 @ 10:48 GMT
Hi Austin,

thanks for your comments. Regarding the mirror test, as I said to Georgina above, I don't consider passing it necessary to establish the existence of a sense of self---it's the other way around, passing the mirror test necessitates having some idea that there is an object in the world that is picked out by the indexical 'I'.

But it's certainly plausible (indeed, likely) that such an 'I' might exist without an ability to pass the mirror test. For instance, I can easily imagine a person that has never encountered the idea of a mirror, or reflection in general, having problems recognizing themselves as their reflection. That doesn't mean they have no concept of themselves.

I agree, though, that my phrasing in the essay was ambiguous at best.

In regard to fractals, I discussed them in passing in an earlier version of my essay, which however had to get cut due to length constraints---basically, the idea was that one can think about fractal structures that contain the full information about themselves within a proper part, so that the part may 'know' the whole. But it ultimately became too lengthy a distraction.

As for early-life memories, I can't really speak to that---I don't have any, and I know virtually nothing about the neurophysiology etc. involved. Georgina above, however, reports being self-aware at birth---maybe you two could exchange early-life experiences!



austin fearnley replied on Jan. 14, 2018 @ 22:41 GMT
Hi Jochen

Thank you for your reply.

You remark connecting fractals with having the full picture in a small part was interesting as was your trimming down on fractals in your essay to meet the essay length restriction. I had to trim but kept quasi-fractals as central. I cut down on quantum spin though and that was a useful enforcement as I think there is a big mystery in tieing spin into the geometry of spacetime and I did not want to get bogged down in that mystery.

I noticed you commented on Indra's Net by Stoica. I may comment there when I am clearer, but to be honest I had not made the connection between quasi-fractals and bohmist ideas before now (so thank you as it has made me think differently!). Bohmism and the Indra's Net (may) imply a continuing spatial connection over time whereas I had been thinking only of an initial symmetry across space which breaks down via symmetry breaking because the initial symmetry is not maintained over time and space. On the other hand my model has 'universes' embedded in particles so maybe it is not surprising that particles have connections across the whole. That sounds unusual but it is simply calling the manifolds (at the heart of particles) 'universes' rather than folded dimensions.

Thanks again.

Austin

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Alan M. Kadin wrote on Jan. 15, 2018 @ 14:11 GMT
Dear Dr. Szangolies,

I read your interesting essay on modeling the universe. But I think you left out an important requirement. Fundamental models must be simple and unified, as recognized by Occam’s razor. Unfortunately, too many would-be fundamental models are anything but simple and unified.

In my own essay, “Fundamental Waves and the Reunification of Physics”, I argue that unity and simplicity are most fundamental, although the unity of physics was broken in the early decades of the 20th century. I review the historical basis for this rupture, and go on to present the outlines of a neoclassical synthesis that should restore this unity.

Briefly, quantization of spin in real quantum waves such as the electron (there are no point particles) provides the scale of discreteness in what is otherwise a universe of classical continuous fields. There is no need for Hilbert space, indeterminacy, or entanglement. The same waves provide a real embodiment of time, space, and relativity; there is no need for an abstract spacetime.

Furthermore, the advent of quantum computing takes this beyond obscure philosophy into the technological realm. Without entanglement, quantum computing will not work. There are billions of dollars being invested in this, and I expect an answer within 5 years. But when I have tried to discuss this with active participants in the field, they react as if I am killing the goose that is laying the golden eggs. No one wants to hear such a negative story, including funding agents. My prediction is that the failure of quantum computing will lead to a reassessment of the entire foundations of quantum mechanics.

Best Wishes,

Alan Kadin

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Author Jochen Szangolies replied on Jan. 17, 2018 @ 18:06 GMT
Dear Alan,

thank you for reading my essay and commenting. Occam's razor is certainly an important methodological guideline in scientific model building, but one should not overextend its reach---otherwise, one risks it loosing its edge. Ultimately, the what the razor really does is guarantee predictivity: without it, we would be free to choose whatever ad-hoc hypotheses make the 'prediction' we want to have, and science becomes arbitrary.

In other, less empirical domains, however, Occam's razor becomes mostly a question of aesthetics.

Regardless, I'll have a look at your essay---however, a point in advance is that it's by no means certain that entanglement is really necessary for quantum computing: DQC1, for instance, is a proposal for quantum computing that does not rely on entanglement to achieve a speedup over what's classically possible.



Eckard Blumschein replied on Jan. 18, 2018 @ 09:11 GMT
Dear Jochen Szangolies,

While you are in Düsseldorf and not in Vienna, I guess you are equally competent in quantum theory as is Quantinger. Therefore I guess that your utterance

"is that it's by no means certain that entanglement is really necessary for quantum computing: DQC1, for instance, is a proposal for quantum computing that does not rely on entanglement to achieve a speedup over what's classically possible"

relates to several essays of this context.

Could you please explain how DQC1 is proposed to work? I guess, QC stands for Quantum Computer. If I recall correctly, at least two decades ago, first systems including quantum computing parts were claimed having already achieved a considerable speedup.

Curious,

Eckard

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Cristinel Stoica wrote on Jan. 15, 2018 @ 20:18 GMT
Dear Jochen,

I enjoyed reading your essay. I like some ideas like the infinite regress in the relation between an object and its model, I thing you made a good point. Also the way you reported them to the four verses by Lao Zi, and the interpretations. As one major point of your argument, I understand that you connect the impossibility to give an accurate description of reality to another major problem, the hard problem. That's an interesting approach to this, and the indeed "bold hypothesis that these connections are given by our phenomenal experience, the qualia: our mental models are connected to objects in the world via our phenomenal experience of them" is quite intriguing!

I may come back with some questions, but until then, good luck!

Best wishes,

Cristi

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Author Jochen Szangolies replied on Jan. 17, 2018 @ 18:12 GMT
Dear Cristi,

thanks for your comment! You're right that the infinite regress is a core element of my essay; ultimately, I fell that much gets explained once one stipulates (or buys my regress argument) that the world isn't computable. And in the end, we never had any good reason to believe it is, anyway.

This leads to the idea that modeling itself is something not amenable to modeling---ultimately, because computation must be grounded in something non-computational, or face infinite regress. I thought it intriguing how these ideas reflect certain tenets of Daoism and Buddhism---in particular in the way they lead to the stipulation that ultimately, the world does not have a 'fundamental nature'---it is 'empty', as the Buddhists would say.

But again, there's a lot of interpretive license here. The Buddhists didn't really think in terms of algorithmic information content anymore than Democritus thought about quantum mechanics when talking about atoms and the void.

I'd be glad to answer (or try to, or at least, be hopefully entertainingly stumped by) any questions you have!




Joe Fisher wrote on Jan. 15, 2018 @ 21:06 GMT
Dear Dr Jochen Szangolies,

You neglected to mention that all real objects have complete visible surfaces.

You wrote: “The world itself, however, cannot be reduced to such a set of fundamental facts. The salient fact here is the necessary incompleteness of every model of the world.”

My research has concluded that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

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Edwin Eugene Klingman wrote on Jan. 17, 2018 @ 04:40 GMT
Dear Jochen Szangolies,

I enjoyed your essay on modeling and generally agree with your statements therein. I too have long thought that an appropriate metaphor is

"The nameless is beginning of heaven and earth,

the named is the mother of 10,000 things
."

and I fully agree with your final sentence:

"… Some of the most difficult philosophical problems might call not so much for their solution, as for their dissolution."

"When the one mind is not disturbed,

The ten thousand things offer no offense
."

One nagging philosophical problem arose from Einstein's contention concerning "the relativity of simultaneity". My essay examines the historical evolution of his view. I hope you will find interesting enough to comment on.

Congratulations on a pleasing and well-written essay.

Best regards,

Edwin Eugene Klingman

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Author Jochen Szangolies replied on Jan. 17, 2018 @ 18:20 GMT
Dear Edwin,

I'm happy you see some value in my appropriation of Laozi. I think that there's a set of similar ideas that you can see popping up throughout history, in really disparate places, that formulate in different frameworks similar core insights---and that, once recognized, those ideas can serve to correct what I see as some fateful and potentially misleading ideas in traditional Western philosophy. Most notably, a core strain in the latter is that everything starts with substance, something that, in some way, is capable of standing on its own, of yielding a foundation not itself upheld by anything else. Eastern metaphysics, with its emphasis on relationalism or denial of such things as fundamental substances, natures or characters, may help overcome some long-ingrained prejudice here.

That's not to say that those wise ancients got everything right. Nobody did, and likely, nobody will for the foreseeable future; but we need to survey all the options on the table, pick what works and discard what doesn't, even if it hurts sometimes, if we ever want to get down to business.

Anyway, thank you for your comment. Your essay is on my reading list, although I may be slow to comment due to some work related issues; I remember finding your last one very intriguing.




Aditya Dwarkesh wrote on Jan. 17, 2018 @ 10:57 GMT
Dear Jochen,

You have constructed, in my opinion, a remarkably accurate analysis of the question at hand. Your essay is certainly one of the standouts in this contest, as far as I am concerned. You will find me to be in agreement with all of the proposals you have put forth, bar none.

Would you happen to have read the works of Ludwig Wittgenstein? I see heavy shades of his own thought in your essay, and Wittgenstein is always welcome company in such meditations.

I have just one query, however: You speak of the minimum amount of information required to uniquely specify a system. Do you have any suggestion for a criterion using which one may pick out this set of information?

My own thoughts (which you will find in my now uploaded essay) are, it seems to me, quite similar to yours (in form than in substance)- I felt like I was rating my own essay when I rated yours!

Regards,

Aditya

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Author Jochen Szangolies replied on Jan. 17, 2018 @ 18:27 GMT
Dear Aditya,

thanks for your kind words! And you're right to spot the influence of Wittgenstein on my thinking (although more the Tractatus, early-period Wittgenstein). As I said above, I think there's a cluster of ideas related to the unutterable, to what cannot be grasped with the concepts we have at our command, that surfaces in different formulations and with different thinkers.

As for the minimum of information, I'm leaning on a concept from algorithmic information theory here: Kolmogorov complexity, which roughly relates to the shortest program (on any kind of computer---in fact, it turns out to be irrelevant which computer you use) that suffices to reproduce a given object. So for a piece of text, or a picture, or whatever, there are generally many possible programs that produce it as output; you take the shortest, measure its length in bits, and get a unique measure of the amount of information needed to specify that system.

It comes with a catch, though: due to issues related to the halting problem, it's in general impossible to compute the precise minimum value. (However, certain approximations exist.)

I'll certainly have a look at your 'linguistic turn' on the contest's question!



Joe Fisher replied on Jan. 18, 2018 @ 15:36 GMT
Dear Jochen Szangolies

In qualifying the aim of the ‘What is Fundamental?’ essay contest, Dr. Brendan Foster, the FQXi.org Science Projects Consultant wrote: “We invite interesting and compelling explorations, from detailed worked examples through thoughtful rumination, of the different levels at which nature can be described, and the relations between them.

Real Nature has never had any finite levels.

I have concluded from my deep research that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

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