Christi,

at the end I had the chance to read your essay. Sorry to be late but this year everything is totally different.

Thanks for the wonderful essay which I gave my highest possibel vote.

I'm glad that we agree that relations are more important, also relations between relations (as often used to define a mathematical structure).

You wrote also about onsciousness and its reducability. I also analyzed onsciousness from a math point of view. Here, onsciousness is also purely relational and I'm not sure that the fact that it consists of matter is important.

See the paper

Best wishes Torsten

    Very nice essay! Clearly written and interestingly argued. Aesthetically the prettiest-looking essay I've seen. I like the use of blue for various headings/citations, and the figures you produced are all very beautiful and clear.

    The point about Wolfram's Rule 110 cellular automaton was strikingly mind-boggling. I can't even object on the grounds that there is some infinity-related trick being used, because the set of all sequences of conscious thoughts (given finitely many brain states and finite human lifetimes) is finite...

    I agree that science is all about relations. The idea of a particle's mass, for example, is only meaningful insofar as it helps us predict how a particle will behave when interacting with other particles. But on the other hand, this makes me worried when it comes to consciousness. I feel like the hard problem of consciousness is deliberately posed to exclude all scientific investigation (experimental, modeling, etc)---like you said, if you can measure it, it's not part of the 'hard' problem anymore.

    Maybe I did not read carefully enough, but I am not sure I understand the consequences of your argument. How can the collection of all true propositions about the world, and the collection of facts about sentient experience, be equal? Does that mean the world may be one big collective dream?

    John

      Dear Cristinel,

      Glad to read your work again.

      I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

      "Interested especially in the geometric aspects of the physical laws".

      It is necessary to understand that all elements of matter from the micro- to macroscales have a quantum and fractal structure of their geometry. This is given and experimentally confirmed in my work.

      While the discussion lasted, I wrote an article: "Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus", due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 "Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability".

      I hope that my modest results of work will provide you with information for thought.

      Warm Regards, `

      Vladimir

        Peter,

        Thanks for visiting my page and reading the essay and for leaving interesting comments.

        > "I also agreed much of your thinking on consciousness, very much in line with my own in my essay 2yrs ago, though I did actually describe a 'what is' ontological layered feedback mechanism which could replicate it. Speculative of course but its architecture is similar to the latest advanced AI."

        This sounds impressive.

        > "Nicely written, but I was left wondering about the connection with the topic, which seemed to be rather obtuse. None the less good on all other scoring criteria and nothing I feel the need to take issue with."

        The central starting point of my essay is that, since science can only deal with relations,

        1. The nature of things is undecidable from within science, which is only about relations.

        2. The nature of experience is undecidable from within science, which is only about objectively and independently verifiable.

        So it's very topical I think.

        Despite this undecidability, I take the hypothesis that sentience is fundamental and show that some of its variants make empirically falsifiable predictions.

        > "I hope you may get to mine, very fundamental in allowing is 'what is' approach, identifying sound evidence for a simple physical mechanism for uncertainty at 'measurement' momentum exchange!"

        This sounds very appealing!

        Cheers,

        Cristi

        Dear Torsten,

        Thank you for reading my essay and for the comments!

        > "I'm glad that we agree that relations are more important, also relations between relations (as often used to define a mathematical structure)."

        Yes, both what we can talk about and what can be made into a mathematical structure are relations of various arity and including between relations.

        > "You wrote also about onsciousness and its reducability. I also analyzed onsciousness from a math point of view. Here, onsciousness is also purely relational and I'm not sure that the fact that it consists of matter is important."

        If something is reducible to relations only, its material substrate shouldn't matter. My point is that, when it comes to consciousness, reducibility to relations corresponds to the "easy problems". Thank you for the link to your article!

        Thanks again for the comments, and good luck in the contest!

        Cheers,

        Cristi

        Dear John,

        Thank you for the comments and for reading my essay!

        > "The point about Wolfram's Rule 110 cellular automaton was strikingly mind-boggling. I can't even object on the grounds that there is some infinity-related trick being used, because the set of all sequences of conscious thoughts (given finitely many brain states and finite human lifetimes) is finite..."

        I agree with you.

        > "I agree that science is all about relations. The idea of a particle's mass, for example, is only meaningful insofar as it helps us predict how a particle will behave when interacting with other particles. But on the other hand, this makes me worried when it comes to consciousness. I feel like the hard problem of consciousness is deliberately posed to exclude all scientific investigation (experimental, modeling, etc)---like you said, if you can measure it, it's not part of the 'hard' problem anymore."

        Part of the reason I constructed this argument was to explain the fact that there is a hard problem, and it's not just some way to move some cherished belief in a gap where science momentarily didn't arrive yet. Nothing has changed in the definitions of sentience as a result of the advance of science. I mean, people always identified it with something unreachable by objective means. But, what I also try to bring with this essay, is that some variants of the hypothesis that sentience is fundamental make empirically falsifiable predictions. More details in my longer essay.

        > "Maybe I did not read carefully enough, but I am not sure I understand the consequences of your argument. How can the collection of all true propositions about the world, and the collection of facts about sentient experience, be equal? Does that mean the world may be one big collective dream?"

        In my longer essay I analyze more possible relations between P and S. Here I mention one of them, which is the simplest that solves Problem 2, of unifying the ontologies of P and S. One way to interpret it would be the one of a big collective dream that you mention, but I think this metaphor wouldn't do justice to the proposal that P=S. First, as we explore deeper the physical world P, we realize that at finer grained levels things are not how they seem at the coarse grained level, and in fact are very different from what we used to think. I expect nothing less from exploring S. So in this case, "dream" is just some manifestation at the coarse graining of S. And even so, "just a dream" assumes that we have any clue what dreams are, but we don't really know. We hallucinate even when we are awake, but we do it in a consistent way in tune with the others, and our brains create representations that we describe to others and since we all use them, we think reality is like this. But this is what we think it is, see endnote 5 of my essay. A distinguishing characteristic of dreams is that they are unstable and inconsistent, while the world P seems rather consistent and persistent. P=S would not break this persistence and consistency, it would just provide it with an ontology, one able to endow it with experience, rather than a cold dead ontology.

        Thanks again for your excellent observations, and good luck with your essay!

        Cheers,

        Cristi

        Dear Vladimir,

        Thank you for reading my essay and for the interesting observations.

        > "I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

        I'm just a neural network, with all the inherent biases and training-dependency features, that work well in some setting but fail in other settings. At least from the point of view of P. So what may seem abstract or concrete in my thinking depends on the context and the interlocutor, of course.

        > "It is necessary to understand that all elements of matter from the micro- to macroscales have a quantum and fractal structure of their geometry. This is given and experimentally confirmed in my work."

        This seems very interesting to hear more about it.

        > "While the discussion lasted, I wrote an article: "Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus", due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 "Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability"."

        Thank you for sharing this here!

        Best luck with your essay and with fighting the pandemics!

        Cheers,

        Cristi

        Dear Professor Cristinel Stoica,

        I found your line of reasoning demonstrating the hard problem of consciousness in fact exists, and its centrality to our conception of reality using arguments grounded in mathematics both ingenious and beautiful.

        I will keep a copy of your work for further reading, and references ( if any circumstances arise).

        What also pleases me is that I sense in between your work and ours ( link: https://fqxi.org/community/forum/topic/3563) we share mutual ground, and we conclude indeed limitations of mathematics are equivalent to limitations of natural science along very similar lines of reasoning; something which you nicely summarize as:

        "But even if we would know with what mathematical structure our world is isomorphic, it

        wouldn't mean we would know everything, because our knowledge can only be expressed in a finite

        number of axioms, and our proofs can only have finite length. Our knowledge will always be limited

        by G¨odel incompleteness (G¨odel, 1931) and Turing's noncomputability result (Turing, 1937)."

        Indeed we share a similar stance to what you have said, "Science

        is a way to decode the book. It proceeds by identifying various words in various contexts, and

        the result is a dictionary, along with some grammar rules. Each word in the dictionary is defined

        in terms of other words, but there are no primary words whose meaning we understand. All the

        definitions in the dictionary are eventually circular. And the grammar rules, which correspond in

        this metaphor to the laws and principles we propose to describe the world, are purely syntactical.", and propose a grand lexicographic project for constructing a complete dictionary for Nature.

        We hope you have time to read our work!

        And thank you for your marvelous entry and the joy and insight we found in your work is reflected in our rating!

        Kind Regards,

        Raiyan Reza, and Rastin Reza

          Rayan, Rastin,

          I couldn't disagree with you more as I've openly disagreed with Cristi also.

          First, if you analyse carefully this his statement you quoted : "But even if we would know with what mathematical structure our world is isomorphic, it wouldn't mean we would know everything, because our knowledge can only be expressed in a finite number of axioms, and our proofs can only have finite length. Our knowledge will always be limited by G ̈odel incompleteness (G ̈odel, 1931) and Turing's noncomputability result (Turing, 1937) you could right away notice many anomalies:

          1. It's not even grammatically correct ( "But even if we knew everything...it wouldn't mean... " is the correct syntax in English but Cristi is grammatically thinking in his mother tongue so I can understand and overlook the root of his error.

          2. It's logically inconsistent since Gödel's results express exactly the opposite, namely, the even in mathematics there can never be a complete and self-sufficient system of knowledge grounded on a finite set of axioms, therefore mathematics is inexhaustible in itself. Chaitin, for instance, went even further to assert that mathematics as such, after Gödel, is ruled by uncertainty and randomness just like the one discovered in QM. He could be right in the sense that whenever and wherever actual infinity pops up(especially since Cantor open the way in set theory)so does uncertainty and randomness, so in a way, the so-called hidden order that science strives to discover in the Universe, seems paradoxically to be both opposed to randomness/chaos/disorder and necessary to it!...

          3. Finally, it's semantically meaningless because it's a speculative and arbitrary hypothesis about an isomorphism of 'nothing concrete' with something abstract, that is, a clearly defined concept of a mathematical structure such as a topological or metric space for instance that are not only rigorously defined axiomatically.

          Dear Mihai Panoschi Panoschi,

          Thank you for your response!

          Since you disagree with Professor Cristinel Stocia, you should direct your disagreements to them.

          Grammar errors and such are something I can look over. I am also failing to see how the statement goes against Godel's Incompleteness Theorems and its computational analogue, Turing Machine.

          To quote you, "It's logically inconsistent since Gödel's results express exactly the opposite, namely, the even in mathematics there can never be a complete and self-sufficient system of knowledge grounded on a finite set of axioms, therefore mathematics is inexhaustible in itself."

          Actually, Godel merely says if a formal system can express or encode arithmetic then it cannot prove its self consistency with a finite set of axioms. So if a finite set of axioms strong enough to encode or interpret arithmetic is incomplete in the sense we will have statements which we cannot decide it is true of false with the statements we have. Which is what Professor Cristinel Stocia's clearly states; if there exists a mathematical structure isomorphic to our physical reality, we cannot prove its self consistency. The implicit assumption is that such a structure much include formal systems strong enough to encode or interpret facts about arithmetic. They state, " Our knowledge will always be limited by Godel incompleteness (Godel, 1931) and Turing's noncomputability result (Turing, 1937)". It is very clear to those familiar with Godel and Turing's results. The limitations are we cannot verify the consistency of the mathematical structure.

          As for the hypothesis being unfalsifiable, that itself is not true. Read Principle 2, "The collection of all true propositions about our physical world admits a mathematical model"

          Thus, if have a mathematical model ( which we can derive from the said mathematical structure), that produces all the true propositions as verified through observation, measurement, and experiments we have a way of connecting the mathematical structure to the physical world. Whether or not they are the mathematical structure itself is a useful abstraction or actually exists is a separate question.

          Professor Stocia cites Tegmark, and I think if you refer his work you would fine a more detailed explanation of a mathematical structure, how it is corresponds to our physical world ( by doing a set of mathematical operations deriving physical symmetries) and such.

          Again, I am no expert here, but the extend Professor Stocia detailed her work, and from what I know I see and understand I cannot detect any "anamoly", and grammar errors while unfortunate is something I have no interest in penalizing someone for.

          Kind Regards,

          Raiyan Reza

          Dear Raiyan and Rastin,

          Please call me Cristi.

          >I found your line of reasoning demonstrating the hard problem of consciousness in fact exists, and its centrality to our conception of reality using arguments grounded in mathematics both ingenious and beautiful.

          Thank you very much for reading my essay and for your insightful remarks.

          >I will keep a copy of your work for further reading, and references ( if any circumstances arise).

          I would recommend the longer one, The negative way to sentience, in case you are interested.

          >What also pleases me is that I sense in between your work and ours [...] We hope you have time to read our work!

          You definitely made me interested to hear more about your essay!

          Thanks again for the visit, and I wish you good luck in the contest!

          Cheers,

          Cristi

          Mihai,

          Thank you for the lesson in English grammar, dully noted! I am also flattered by your attention with the second part of your comment. May I remind you that I defined what a mathematical structure is in my essay, and I also even gave you a link in replies to some of your comments, where you mistook it for "a mere representation of our minds" (which is not what I mean). Now you are mistaking mathematical structure for an axiomatization of it (which, again, is not what I mean, and I'm pretty sure Plato didn't mean this either!). As an example, think of the set of natural numbers, along with the operations of addition and multiplication defined as subsets of NxNxN. This is an example of a known mathematical structure. Now think at some axiomatization of it, and Gödel's incompleteness theorem, and see why the structure can be known, yet not everything about natural numbers can be known.

          Cheers,

          Cristi

          Raiyan,

          Wittgenstein warns and teaches us that grammar/syntax plays an important role within the semantic universe of a given language. The "If Clause" in English has a very precise and well defined temporal structure that we need to pay attention to when we write something of (supposedly) importance such as a scientific essay. For instance, I again fail to comprehend what you're trying to say in this sentence: "Thus, if have a mathematical model ( which we can derive from the said mathematical structure), that produces all the true propositions as verified through observation, measurement, and experiments we have a way of connecting the mathematical structure to the physical world. Whether or not they are the mathematical structure itself is a useful abstraction or actually exists is a separate question." and what type of "If Clause" you're trying to use...

          Since it is not a clear cut of a cause/effect type 0 relationship like in "if it rains, the ground gets wet", and it's something more hypothetical and problematic, I think what you're trying to say is that " Thus, if we had a mathematical model....then we would have a way..." which for me resembles more of a wishful naïve thinking rather than serious logical argumentation with its further implications.

          But maybe you're trying to say something else in which case I may be wrong but we'll both agree that in both cases correct grammar plays an important role for our understanding to have a common starting ground and thus make the transfer of ideas between two minds possible. So, it's not necessarily about penalising but about comprehension and communication of our thoughts mostly.

          Dear Cristi,

          I am very glad to see that your essay is doing well.

          I really enjoyed it!

          The consciousness question is both difficult and fascinating. And I think that the fact that we have so much of ourselves invested in the solution does not help us to attain an honest understanding.

          I have long thought that consciousness arises from the brain modeling (describing ) itself, which is inherently self-referential. If so, we should expect some element of strangeness or surprise. What precisely that would be, I am not in the position to say. That by itself would be an interesting question. What predictions could this hypothesis (that the brain describes itself) make? Certainly, answering this is necessary for falsifiability.

          I would agree that science focuses on relations and not things.

          This really is the essence of my work on Influence Theory, which has shown greater promise than I had originally expected.

          In that work (Influence Theory), we make it clear that the only properties that one can know about are those properties that affect how an object influences others. Despite the validity or invalidity of Influence Theory as a foundational theory, I still believe that this idea is correct.

          So what does this say about Consciousness in terms of it being a result of relations or substance?

          Well, if consciousness is a property that arises from properties of a substance, then we can only know about this property consciousness because it affects how objects influence one another. In fact, further thought reveals that the characteristics of that property are defined (operationally) by the affect it has on such influence. Since influence is a relation, and that is the only means we have to know about or describe properties, then consciousness cannot really be the result of a property of a subtance, because it would be indistinguishable from the property of any other substance that affected influence in an identical manner.

          So, I would have to conclude that consciousness must arise from relations, like most everything else.

          I'd like to hear your thoughts on that.

          As for me, I still think that consciousness arises from the brain modeling itself.

          Thoughts??

          Thank you, again, Cristi, for your enjoyable and thought-provoking essay!

          Sincerely,

          Kevin

            Dear Cristi,

            I really enjoyed reading your essay to cover several academic fields.

            In Section 5, you discussed the relationship between thermodynamic context and information theory or computational viewpoint. In the past essay contest, I wrote the specific part of this fundamental question as seen in my past essay. Your point is reductionism. Is this related to the operationalism?

            Best wishes,

            Yutaka

              Dear Cristi,

              Thanks for replying and sharing the longer version of your work, we will read it with great interest!

              We wish you all the for this essay contest and research!

              Raiyan and Rastin

              Dear Professor Mihai Panoschi Panoschi,

              I apologize for missing an honorific in my first response.

              Thanks for replying and your thought provoking comments!

              That said, yes I fully agree grammar and syntax play an important part in semantics of sentences and indeed cited Wittgenstein in my own work to advocate my stance, though I by no means claim your level of expertise or depth.

              Having said that, in day to day conversation we rely on "informal" systems to communicate.

              Unless you propose to reduce everything we have said to a formal system ( which is time consuming) than some degree of leniency on regards to grammar, and syntax is warranted, even in scholarly works.

              That said, I am confused you attribute cause/effect to the sentence, "If it rains, the ground gets wet". Implication is not causation, something I remember being from my Discrete mathematics course. Let us attribute false value to the proposition p," it rains", and truth to the proposition ," the ground gets wet", the truth value for p implies q would still be true. However, a causal understanding would tell us a different scenario.

              Again, thanks for your detailed critique and replying here!

              All the best for this essay contest and researches! And, I suppose apologies for semantic ambiguity and resembling "naive wishful thinking".

              Best Wishes,

              Raiyan Reza

              This paper was fun to read Cristi...

              I'm grinning right now like someone who looked in the back of the book in the section called 'solutions to problems.' Or maybe I've just been actively exploring the other side of the coin from what you set out. If Science is only in the realm of relations and theory arises only in the form you describe; what I have been doing is not Science nor theoretical Physics.

              Instead; I discovered something in pure Maths that boggles the mind, almost by accident while trying to find something else, and as with Haldane struggled for years to understand what I had discovered and to learn its relevance. I spent 33 years grappling with questions like "Why does it explain so much?" and more recently with "How do I avoid getting scooped again?" when someone comes out with a theory proposing something I'd learned years ago.

              For the record; I do think consciousness is primal, or essential. I think the evolution of consciousness is possible to express mathematically, however, or resides naturally in the octonions as the vehicle for projective geometry, the geometry of perspective and hence of observation. I have just published a collection of "Octonion Poetry" (link below) with a section explaining how that algebra explicates the dynamic of involution and evolution, leading to a specific syntax and yielding sentences that sound like aphorisms or poetry.

              "One, open, as multiplicity and formless nothingness, finds peace in true relation, and knows all as self." - J. Dickau

              So if true; this means that consciousness cannot arise by its local relations alone, but only in relation to the whole, or global relations. One can think about this in terms of Misner, Thorne, and Wheeler, chap 44 sec 5, talking about pregeometry as the calculus of propositions. Oneness --> openness --> postulation --> repetition, and so on. The same words can serve as a formula for quantum gravity or for the evolution of consciousness. It's kind of a personal credo for me, but it is suitable for scientists. Proceeding as if we are a multiplicity of things and a sea of nothingness between them acknowledges reality as it is.

              Anyhow; you get high marks from me, and you leave me with about 144 more pages of comments to make. So I'll leave off here for now.

              Regards,

              Jonathan

              Unity, Oneness & Numbers: Octonion Poetry

                Dear Kevin,

                Thank you for visiting and reading my essay, and for the excellent question.

                > "In that work (Influence Theory), we make it clear that the only properties that one can know about are those properties that affect how an object influences others. Despite the validity or invalidity of Influence Theory as a foundational theory, I still believe that this idea is correct. So what does this say about Consciousness in terms of it being a result of relations or substance?"

                As my argument aims to prove, if consciousness is 100% reducible to relations, then one must also admit that a rule 110 cellular automaton with suitably chosen first row can have consciousness. This despite being a flat timeless tapestry. There are certainly people who think this, and even I take this view as true about anything that ignores sentient experience. And there are people who don't accept this, because they know that they are in a way beyond the mere relations, roles in society, processes, computation etc. Relations are about the "easy problems". And, while I agree that the behavior of consciousness, and all of its relations, including the causal relation that makes Descartes say "I am", are, of course, 100% reducible to relations, like the structures P and S mentioned in my essay, my whole claim is that this is not what makes experience possible. This is what makes conscious-like behavior possible. By sentience I understand what makes experience possible, its nature, its ontology. So consciousness is 100% relations by any objective and independently verifiable means, yet it's 100% sentience by its ontology, which is not accessible by the objective and independently verifiable means. Incidentally, while this position is usually associated to an epiphenomenalist position, I think that it can make testable predictions, so it's falsifiable. And in my longer essay The negative way to sentience I explain what variants of the relations between P and S correlate to what interpretations of Quantum Mechanics, and that some of them make testable predictions. If you are interested in this issue, I'd very much appreciate some comments to that longer essay, especially since you take the position that you take. No rush with this. And who knows, maybe you'll find the more elaborate arguments more compelling ;-) Or maybe you'll change my mind (just kidding about the latter, I doubt everything I think, except for the fact that I am sentient).

                Thanks again for the insightful comments!

                Cheers,

                Cristi

                Dear Yutaka,

                Thank you for reading my essay and for the interesting comments. You mention a past essay of yours, I read it at that time and commented. I look forward to read your current one.

                > "Your point is reductionism. Is this related to the operationalism?"

                I am not sure that my point is reductionism per se. I am fully for trying to push reductionism to its natural limits as much as possible. I discussed these limits in a previous essay. As for the relations with operationalism, there must definitely be such relations. And I take here the position that science cleaned of all of its assumptions is about relations only, which is close to operationalism. I am not an adept of operationalism in my work though. And particularly when talking about sentience, I think sentience (stripped of all form and relations) is what's beyond relations.

                Cheers,

                Cristi