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**Luca Valeri**: *on* 5/13/20 at 22:04pm UTC, wrote Hi John, no need to apologize. I have read the essay really quick. So it...

**James Hoover**: *on* 5/12/20 at 6:18am UTC, wrote John, Hope you have time to check mine out before the deadline:...

**John Schultz**: *on* 5/11/20 at 17:57pm UTC, wrote Hello Luca, My apologies if I was less clear than I thought. I tried quite...

**John Schultz**: *on* 5/11/20 at 17:44pm UTC, wrote Hi Ernesto, I hope I clearly suggested two different plausible meanings...

**Luca Valeri**: *on* 5/11/20 at 13:26pm UTC, wrote Hi John, I like your symmetric distinction of science and pure...

**Ernesto Vaca**: *on* 5/10/20 at 20:41pm UTC, wrote Hi John, I enjoyed reading your essay. It was very clear, and your...

**Steve Dufourny**: *on* 5/2/20 at 18:03pm UTC, wrote You are welcome, I am understanding , we try to capture in Words our ideas...

**John Schultz**: *on* 5/2/20 at 15:46pm UTC, wrote I’m always glad when someone enjoys the ideas I struggle to capture in...

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FQXi FORUM

September 17, 2021

CATEGORY:
Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020)
[back]

TOPIC: A Framework for Thinking about Knowability by John S Schultz [refresh]

TOPIC: A Framework for Thinking about Knowability by John S Schultz [refresh]

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.

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.

Note: This Essay PDF was replaced on 2020-04-20 16:13:00 UTC.

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...

view entire post

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...

view entire post

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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

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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

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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.

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

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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.

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

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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

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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

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

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

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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

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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

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.

post approved

post approved

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

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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

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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

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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

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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

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Regards

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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

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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

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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.

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.

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...

view entire post

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...

view entire post

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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.

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.

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

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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

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John,

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

Jim Hoover.

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

Jim Hoover.

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