Essay Abstract

The loosely defined concept of a pattern seems to provide a fruitful framework for approaching some of the questions about limits on what can be known about the real world. Nature comes in patterns, and patterns can also be studied in their own right, merely as patterns. We will draw a distinction between patterns in Nature and patterns in the abstract, and broaden it to a partial characterization of science and mathematics. Then we introduce a partial taxonomy of pattern types and notice that the various limitative theorems of mathematical logic severely constrain what can be known using algorithmic mathematical patterns, but are not necessarily pertinent to other, non-algorithmic, types of patterns. Next we will use the concept of Free Will to question whether human cerebration is algorithmic. This appears to open the door to a possibility that if human cerebration is non-algorithmic, perhaps we can know the world more completely than the limitative theorems would seem to imply. However, knowing the world would involve knowing what mathematical pattern Nature has chosen, so to speak, for various natural phenomena. That seems to be impossible because, having only finitely many empirical data points about Nature, there should be an intractably large infinity of mathematical patterns that fit the data. Is there a way to cut down on this infinite set? My conjecture is that there is no adequate way, which sounds pessimistic at first blush, but seems to me to be actually quite an optimistic assessment of the path forward.

Author Bio

I graduated from MIT in mathematics almost half a century ago, moved to Vermont to ski, started a school for ski racers (Green Mountain Valley School) and a string of other small businesses. My current business is Super Thin Saws.

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Dear John S Schultz,

A brilliant observation that, while mathematical logic severely constrains what can be known using algorithmic mathematical patterns, it is not necessarily relevant for other, non-algorithmic types of patterns.

You say "this appears to open the door to a possibility that if human cerebration is non-algorithmic, perhaps we can know the world more completely than the limitation theorems would seem to apply."

You might appreciate the first paragraph on page 8 of my essay Deciding on the nature of time and space.

The history behind that paragraph is the reason that I deeply appreciate your observation that the limitation [math] theorems,... born from the study of algorithmic patterns... have no necessary pertinence to non-algorithmic patterns - and thus no necessary limitations on knowability.

You are correct: it is a big claim. I have for years been trying to formulate this as clearly as you do, with no success. I knew it, but could not so clearly state it. I wish I had been able to make your argument in my essay The Nature of Mind, which had the highest community rating in the 2016-2017 essay contest.

In short, human cerebration is not algorithmic, although of course it includes 'logic', hence algorithmic patterns. The mass-density-based flows in axons and across synaptic gaps generate gravito magnetic fields, and the [endless possible] flow configurations of local fields are 3-D and dynamic, and as I posit this field to be the 'consciousness field', wherein lies awareness, said awareness is not algorithmically structured. You have provided a major missing argument to me, and for this I sincerely thank you.

The dynamic mass-density flows in the brain's trillions of possible neural net connections enable 3-D fields capable of physically approximating any 3-D 'shape' and the self-aware field hence internally 'models' the 3-D reality we either observe or imagine [we do both!] We do not algorithmically compute 3-D from xs, ys, and zs. It goes without saying that no other consciousness model has any idea how we obtain 3-D awareness of the world, at all scales.

The local field is, of course, just a very dense, very organized field self-identified with the local brain, but contiguous with the self-aware universe that Wheeler and many others propose. This field, in its densest possible form, is the field to which all known forces are assumed to converge at the creation/Big Bang. If this gravitational/consciousness field is the essence of self-awareness, it was here at the beginning, and has self-evolved through to the present, increasingly self-aware.

This lack of inherent limitation of knowability is why I reject Hodge's claim that it is 'hubris' to claim awareness of ontology.

I hope your essay makes as much sense to others as it does to me. I think it is brilliant. It is the missing link argument for me, that puts consciousness in 'mathematical' perspective.

Edwin Eugene Klingman

    John In my essay "Clarification of Physics...." I introduce the mathematical pattern used to create "nature" ( i.e. the physical world and its contents). This mathematical pattern is isomorphic with nature and can be used to understand and explain the natural world. Are there other solutions to the creation of the universe? Not likely. John Crowell

      Hi John, Your essay is full of food for thought. Well set out and easy to read. Though I did the many abbreviations difficult to remember and had to keep scrolling through the essay to re-find their definitions, as you had not put them all in one place. Kind Regards, Georgina

        I think it is bad form to start with an apology.

        You have no reason to do that, I took a lot from your view and presentation.

        I'm delighted that you enjoyed my approach, and even more delighted that you might find it useful. I'm more or less out straight because of a family health emergency, but I very much look forward to having a look at your essay, once time permits.

        Thanks for your really excellent suggestion. (I'm a little embarrassed not to have thought of that on my own.)

        Hmmm.... You're probably right about that (Are you now expecting me to apologize?) OK. More seriously, I'll keep that in mind for any future essays. Thanks.

        Interesting view point. I'm not sure that I agree with your assessment, but I will enjoy chewing on it.

        Dear Mr. Schultz,

        thank you for this essay, in which, although not fully spelled out in detail, there is interesting food for thought. I wish you good luck in the contest!

        If you have a moment, I would also appreciate if you could have a look at my essay.

        All good wishes,

        Flavio

          John,

          Well done. Extremely cogent and orderly in your argument. I do see that our lack of understanding of the quantum world is a limitation on our accomplishments. You speak of nature as a way of studying the patterns of nature, but the quantum world has a part in all of nature's structures, something we seem to have little of a handle on. Randomness not patterns enters into quantum behavior according to our theories. We all know it is difficult to cover the scope of all 3 of the "Us". Undecidability seems to weigh more squarely on algorithmic solutions. Thought your conclusion was masterful. Your zeroing in on Knowable, its nuances in the science world & its assessments. I think yours is on of the best efforts. My essay seems to parallel many of your ideas.

          My rating is your 5th. I say this because someone is giving 1s w/o comments.

          Jim Hoover

            Thank you Flavio,

            Yes, to be sure, it is only a framework. We would all like to climb the great mountain of truth and understanding. My essay points to signs that seem to say (if you will) that "this path may lead higher on the mountain." But you are correct, I have not furnished a complete guide to the pat, nor have I climbed up there. I am quite glad that you find the signs intriguing.

            Best regards,

            John

            Hello Jim,

            I'm glad you find my ideas interesting. I'll be very pleased if they serve as a good jumping off point for you and others as we all strive for better understanding. If there are some low reviews, that's fine, but I do wish they'd leave comments so I could tell whether it was the ideas, or the exposition of the ideas, that failed to resonate with them

            John

            John Schultz re-uploaded the file Schultz_A_Framework_for_Thi_1.pdf for the essay entitled "A Framework for Thinking about Knowability" on 2020-04-20 16:13:00 UTC.

            Dear John S Schultz

            Thank you for a thought provoking essay with a smooth flow... !!

            What will we do for the scientific processes with out any Pattern? For example, we can see some in quantum mechanics..............

            Best

            =snp

              5 days later

              Hello,

              I liked a lot your essay, you explain with relevance these limitations in making a distinction between patterns in Nature and patterns in the abstract, your introduction for a partial taxonomy of pattern types is very interesting for the ranking in a deterministic way if I can say. That permits to sort and see the real isomorphisms and our limitations. I love the maths and I beleive strongly that without them we cannot prove of course our assumptions, extrapolations, they must utilised with a kind of wisdom because they can imply also with their properties confusions, that is why it is necessary to rank these mathematical properties to see the real deterministic ones. I wish you good luck in this Contest, your essay was a pleasure to read.

              Best Regards

                5 days later

                Thank you for your kind comments. One of the goals in expounding an unusual point of view, of course, is to be thought-provoking. I'm very glad you enjoyed it.

                I'm always glad when someone enjoys the ideas I struggle to capture in words. Thanks for your comments

                You are welcome, I am understanding , we try to capture in Words our ideas , like we formalise them in maths and try to prove our assumptions. Personally I work about my thjeory of spherisation, an optimisation of the universal sphere or future sphere with quantum 3D pshres and cosmological spheres, I consider that all is made of particles and I consider 3 main series finite of 3D spheres having the same number than our cosmological finite serie of spheres, I consider a main primordial serie for the space and two fuels, photons and cold dark matter and when they merge they create the topologies, geometries, matters, particles and fields. I formalise all this puzzle with an intrinsc Ricci flow, the Hamilton Ricci flow, an assymetric Ricci flow also for the unique things probably in the smallest volumes of these series , the lie derivatives, the lie groups, the lie algebras, the Clifford algebras, the topological and euclidian spaces and the poincare conjecture mainly, it is not easy but I try to do my best for this formalisation, I have quantified and renormalised this quantum gravitation with this general reasoning. Don t hesitate to ask details, I will answer with pleasure. Wish you all the best ,

                Regards

                8 days later

                Hi John,

                I enjoyed reading your essay. It was very clear, and your characterization of different pattern types was quite insightful. I had never thought of patterns like that before. I have a hard time imagining what a non-algorithmic patterns would be, especially in a pure sense. It almost seems that without an algorithm, it is not fair to call them patterns, but that is solely based on intuition, and is not highly thought out. Your example of mutation seems true, but chaotic, and chaos strikes me as a lack of a pattern, or at least one too complex for humans to understand, right now at least. Perhaps I need to think more on what you mean by non-algorithmic pattern.

                I think I disagree that there is no adequate way to cut down on the infinitely many mathematical patterns that fit data, because some mathematical structures fit more data than others, and that is one way to cut-down on the possibilities. But based on intuition I do have a sense that science might very well go on forever regardless. We may never be fully right, but we can strive to be less wrong.

                All the best,

                Ernesto

                  Hi John,

                  I like your symmetric distinction of science and pure mathematics. Also it seems natural attach the question about knowability to the study of pattern as our main mental capability seems to be the recognition of pattern. Also very interesting is the distinction of algorithmic and non-algorithmic pattern. The non-algorithmic one you seem connect with random processes. I'm not sure if that is a to strong limitation. Although I couldn't come up with an other idea, what else non-algorithmic could mean.

                  My main critic in your approach is one that became clear to me in the course of a few discussions I had in this contest and that is a bit the topic of my essay. It is a critic on your conjuncture 1a: You postulate (at least implicitly) the existence of real world-patterns. And that they are isomorphic to the mathematical pattern. For me conjencture 1a is a pattern theoretic version of what I call naive or simplistic realism in my essay.

                  But the pattern version is much easier to criticize because it is used as a conjecture in all science and not only in fundamental physics, ,where it is much, much harder to criticize and even to think, the world could be otherwise. (This is what I try to show in my essay).

                  But what I mean by that? Let us take as example the classification of species. Certainly one can say, that there exist pattern, that favour some classification (although the pattern is never fully precise and without ambiguities). On the other hand, one could say that the classification (and the matching pattern) are somehow arbitrary, man made and serve different purposes depending on the field of inquiry: evolution, ethology, ecology, etc. You may say: but as far as these pattern can be found, they are objectively in nature. And have a corresponding mathematical pattern, that describes it. But the pattern to have a meaning and to be recognized as such, needs a context under which it becomes meaning full.

                  Somehow, I. have the feeling the pattern is imposed by us, as something functional and lies not in nature itself.

                  Does this make any sense to you?

                  Luca

                    Hi Ernesto,

                    I hope I clearly suggested two different plausible meanings for the word "pattern," and explained which one I was using. But I'm not too hung up on what string of letters goes with what meaning. If you'd like to suggest alternative terminology, I'm all ears.

                    Mutation is not due to chaos (in the normal technical sense.) If you mean that it can create bedlam (in an informal sense) I guess perhaps it can, but normally I'd say it was the other way around. More importantly, the question doesn't seem relevant to my essay. Perhaps we are misunderstanding each other.

                    And..., well, I guess you are saying that as we get more data we can eliminate some of that infinite number of patterns that fit (ALL) the data points. This is true, of course, but the number that are left wills still be infinite. And that, it seems to me, is one place judgement comes in. Obviously a polynomial equation with a few terms is something useful. A polynomial equation with thousands of terms..., rather less so! So we start with something simple and hope that new data doesn't eliminate it..., at least not too quickly.

                    Hello Luca,

                    My apologies if I was less clear than I thought. I tried quite hard to make a distinction between patterns that are partially random, and some other type that you and I are both unable to come up with an example for. Please reread that section and tell me if it now makes more sense.

                    1a, and ALL the conjectures are merely that. (More or less predictions.) If your intuition thinks otherwise, than our intuitions disagree with each other, which of course is okay. As I said in the closing, this may have sounded anti-realist, but it is not.

                    For your example, I would feel that the pattern exists, and the subjectivity comes from two places. One the one hand, we don't have complete knowledge of the pattern. And on the other hand, we do know an intractably bulky portion of the pattern, and we all have different ways to slice-and-dice it to make it more useful.

                    John,

                    Hope you have time to check mine out before the deadline: https://fqxi.org/community/forum/topic/3396

                    Jim Hoover.

                    Hi John,

                    no need to apologize. I have read the essay really quick. So it is on me, not to have read the careful enough.

                    By the way, my essay is exactly about non algorithmic change of pattern that is not random. This comes like this (I might I misuse your terminology a bit - sorry for that). I impose the following limitation: The input and output must also be describable by the algorithmic pattern. I call this property semantical closed theory. If now a pattern P2 is richer, more complex and contains more pattern than P1. If now P2 follows in time P1. Then P2 cannot be predicted nor described by P1, because of a lack of language. That would be a non algorithmic change of patterns.

                    What do you think?

                    And yes, our intuition disagree and that is fine. And no, you do not sound anti-realist. It is good to know the limits of any realist theory.

                    Good luck in the contest!

                    Luca