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Current Essay Contest

Contest Partners: Fetzer Franklin Fund, and The Peter and Patricia Gruber Foundation

Previous Contests

Contest Partners: Fetzer Franklin Fund, and The Peter and Patricia Gruber Foundation

read/discuss • winners

read/discuss • winners

How can mindless mathematical laws give rise to aims and intention?

Contest Partner: The Peter and Patricia Gruber Fund.

read/discuss • winners

Media Partner: Scientific American

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Which of Our Basic Physical Assumptions Are Wrong?

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RECENT POSTS IN THIS TOPIC

**Pavel Poluian**: *on* 5/16/20 at 12:55pm UTC, wrote We carefully read and discussed everything. There is something to think...

**Kwame Bennett**: *on* 5/1/20 at 20:23pm UTC, wrote Dear Roman, Excellent Essay, please take a look at the long form version...

**Michael muteru**: *on* 4/28/20 at 21:40pm UTC, wrote hi roman I appreciate your comprehension of human observer.Do human...

**Vladimir Rogozhin**: *on* 4/15/20 at 20:05pm UTC, wrote Thank you very much, Roman, for your quick reply and link. I'm starting to...

**Roman Yampolskiy**: *on* 4/15/20 at 19:05pm UTC, wrote Dear Vladimir, Thank you for your kind words and for sharing some...

**Vladimir Rogozhin**: *on* 4/15/20 at 16:58pm UTC, wrote Dear Roman, Your extremely important essay makes it possible to conclude:...

**Roman Yampolskiy**: *on* 3/12/20 at 19:17pm UTC, wrote Dear Flavio, Thank you for your kind words and useful pointers. I look...

**Flavio Del Santo**: *on* 3/11/20 at 16:36pm UTC, wrote Thank you for this well-written and stimulating essay. Let me add...

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A quantum computer composes chart-topping music, programmed by physicists striving to understand consciousness.

A meditating mathematician is developing a theory of conscious experience to help understand the boundary between the quantum and classical world.

FQXi FORUM

December 8, 2022

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

TOPIC: Unverifiability, Unexplainability & Unpredictability by Roman V Yampolskiy [refresh]

TOPIC: Unverifiability, Unexplainability & Unpredictability by Roman V Yampolskiy [refresh]

Optimistic plans of mathematicians to automatically uncover all truths have been thwarted by Gödel’s Incompleteness and Turing’s Undecidability among many other impossibility results. In this essay we describe a more general limitation on mathematical proofs, Unverifiability, along with Unpredictability and Unexplainability of powerful knowledge discovery agents. We conclude with analysis of limits to what we can prove, predict or understand on physics and science in general, as well as safety of artificial intelligence in particular.

Dr. Roman V. Yampolskiy is a Tenured Associate Professor in the department of Computer Science and Engineering. He is the founding and current director of the Cyber Security Lab and an author of many books including Artificial Superintelligence: a Futuristic Approach. During his tenure at UofL, Dr. Yampolskiy has been recognized as: Distinguished Teaching Professor, Professor of the Year, Faculty Favorite, Top 4 Faculty, Leader in Engineering Education, Top 10 of Online College Professor of the Year, and Outstanding Early Career in Education award. Dr. Yampolskiy’s main areas of interest are Artificial Intelligence and Cybersecurity.

I found your essay very clearly written, interesting educational and topical.The idea of equating a mathematics verifier with a physics observer is an interesting one. However I don't fully agree. Physics observers have a partial viewpoint that relates to a particular context and perspective of observation or measurement. So the conclusion is not impartial. Observers with similar viewpoints can...

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Dear Georgina,

Thank you for your kind words and helpful feedback! In a way, different verifiers also come from different contexts, as a particular one is unlikely to contain all of known mathematics, but each one will have some subset, perhaps not fully integrated with all other domains of mathematical knowledge. So their conclusions may also be not impartial, but biased by their...

view entire post

Thank you for your kind words and helpful feedback! In a way, different verifiers also come from different contexts, as a particular one is unlikely to contain all of known mathematics, but each one will have some subset, perhaps not fully integrated with all other domains of mathematical knowledge. So their conclusions may also be not impartial, but biased by their...

view entire post

Dear Roman,

your essay contains much food for thought, and I'll have to take some time digesting its contents. You very deftly eliminate a naive view of mathematical proof, according to which once something's proven, we know it to be true, and that's that.

I wonder about how to extend this framework. Is it, for instance, possible to construct a complexity theory for proofs? Say,...

view entire post

your essay contains much food for thought, and I'll have to take some time digesting its contents. You very deftly eliminate a naive view of mathematical proof, according to which once something's proven, we know it to be true, and that's that.

I wonder about how to extend this framework. Is it, for instance, possible to construct a complexity theory for proofs? Say,...

view entire post

report post as inappropriate

Dear Jochen,

Thank you for reading my work and taking the time to comment. You are suggesting some interesting directions for future work, some of which have been attempted and others are still waiting to be tried. I do try to address such alternatives in the appendix, and will try to do more for your ideas in my future work. Thank you!

Best,

Roman Yampolskiy

Thank you for reading my work and taking the time to comment. You are suggesting some interesting directions for future work, some of which have been attempted and others are still waiting to be tried. I do try to address such alternatives in the appendix, and will try to do more for your ideas in my future work. Thank you!

Best,

Roman Yampolskiy

Dear Roman,

thank you for your answer. I think that it's an interesting thread to consider whether to merely certify a proof, one always needs to be capable of checking whether it is correct. Certain proofs, if you possess them, may enable you to perform certain tasks---hence, your ability to perform these tasks will certify your having that proof, up to any given standard of certainty (strictly smaller than absolute certainty, of course). This sort of thing seems closely related, to me, to the problem of certifying whether one party has a certain capacity (say, access to a universal quantum computer) without the other party necessarily having that capacity (a quantum computer to check).

Therefore, it doesn't seem quite right to me that each verifier necessarily needs capacities equal to or exceeding that of the system it verifies; indeed, there may be ways for you to convince me you've proven something without me having any hope of ever checking the proof, which would indicate that a proof-checker is not the only possible kind of verifier imaginable.

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thank you for your answer. I think that it's an interesting thread to consider whether to merely certify a proof, one always needs to be capable of checking whether it is correct. Certain proofs, if you possess them, may enable you to perform certain tasks---hence, your ability to perform these tasks will certify your having that proof, up to any given standard of certainty (strictly smaller than absolute certainty, of course). This sort of thing seems closely related, to me, to the problem of certifying whether one party has a certain capacity (say, access to a universal quantum computer) without the other party necessarily having that capacity (a quantum computer to check).

Therefore, it doesn't seem quite right to me that each verifier necessarily needs capacities equal to or exceeding that of the system it verifies; indeed, there may be ways for you to convince me you've proven something without me having any hope of ever checking the proof, which would indicate that a proof-checker is not the only possible kind of verifier imaginable.

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You write in your nice expose at the end: our results are very timely and should allow for a better understanding of limits to verifiability and resources required to get desired levels of confidence in the results.

Please, allow me to comment:

The development of Being goes from total unformedness to total formedness.

Observing observes and forms "That which is" as a world. ...

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Please, allow me to comment:

The development of Being goes from total unformedness to total formedness.

Observing observes and forms "That which is" as a world. ...

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Dear Roman V Yampolskiy, after reading your essay, I realized that I should ask you to verify the new Cartesian generalization of modern physics, which is based on the identity of physical space and Descartes’s matter. According to this identity, it is common for physical space to move relative to itself, since it is matter. Arguing in this way, I showed that the probability density of states in...

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Hi Roman,

I like your overview of the reductionist scientific paradigm in his many empirical, theoretical and pratical implications very much. But I personally can't find any deep new conclusions. Correct me if I'm wrong, but couldn't you reduce all scientific concepts to an abstract (turing-related...) 'reduction' and that's really it?

Greetings

Morris

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I like your overview of the reductionist scientific paradigm in his many empirical, theoretical and pratical implications very much. But I personally can't find any deep new conclusions. Correct me if I'm wrong, but couldn't you reduce all scientific concepts to an abstract (turing-related...) 'reduction' and that's really it?

Greetings

Morris

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Hi Roman,

sorry for this long reply. But I was really intrigued by your essay, which inspired me to a lot of thoughts.

In physics I used to be a bit of a Platonist interested only in theoretical physics, which is reflecting the true forms and not much interested in experimental physics that are concerned only with the shadows of ideal forms. In your essay you made the theory of...

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sorry for this long reply. But I was really intrigued by your essay, which inspired me to a lot of thoughts.

In physics I used to be a bit of a Platonist interested only in theoretical physics, which is reflecting the true forms and not much interested in experimental physics that are concerned only with the shadows of ideal forms. In your essay you made the theory of...

view entire post

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Hey Luca,

Thank you for your detailed comment.

“I am not up to date in AI research and I found your exposition very interesting. Were you able to give to 'comprehensibility' a precise mathematical meaning?”

Please see: https://arxiv.org/abs/1907.03869

“But could two minds that have the same amount of states comprehend each other?”

Please see: https://arxiv.org/abs/0708.1362

“In your physics section you seem to imply that the probabilistic nature of mathematical verification implies the probabilistic nature of mathematics and hence the probabilistic nature of physics (=QM) in the MU. Is that so?”

Yes, that is one of my ideas.

Best,

Roman

Thank you for your detailed comment.

“I am not up to date in AI research and I found your exposition very interesting. Were you able to give to 'comprehensibility' a precise mathematical meaning?”

Please see: https://arxiv.org/abs/1907.03869

“But could two minds that have the same amount of states comprehend each other?”

Please see: https://arxiv.org/abs/0708.1362

“In your physics section you seem to imply that the probabilistic nature of mathematical verification implies the probabilistic nature of mathematics and hence the probabilistic nature of physics (=QM) in the MU. Is that so?”

Yes, that is one of my ideas.

Best,

Roman

Dear Roman,

Thank you for disentangling all these different limitations of human knowledge.

Science made great strides by formulating the intuitive notion of a computation with a Turing machine. With this formulation, we were able to conquer the notion of undecidability. It would be nice to formulate the many intuitive concepts you bring to light.

You have a line:...

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Thank you for disentangling all these different limitations of human knowledge.

Science made great strides by formulating the intuitive notion of a computation with a Turing machine. With this formulation, we were able to conquer the notion of undecidability. It would be nice to formulate the many intuitive concepts you bring to light.

You have a line:...

view entire post

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Dear Noson,

Thank you for your comment. You are asking great questions about how IQ of multiple agents can be combined. This week, a book chapter of mine (chapter 1: TOWARDS THE MATHEMATICS OF INTELLIGENCE) on this topic is out in the book: https://vernonpress.com/book/935 I think it answers some of your questions, but still leaves much room for future work.

Best,

Roman

Thank you for your comment. You are asking great questions about how IQ of multiple agents can be combined. This week, a book chapter of mine (chapter 1: TOWARDS THE MATHEMATICS OF INTELLIGENCE) on this topic is out in the book: https://vernonpress.com/book/935 I think it answers some of your questions, but still leaves much room for future work.

Best,

Roman

Thank you for this well-written and stimulating essay.

Let me add something to your sentence: “The Born rule [76], a fundamental component of Copenhagen interpretation, provides a link between mathematics and experimental observations.” . I would like to point out to you that the interpretation known as QBsim, whose author explicitly consider a refinement of Copenhagen, takes the Born rule as an element of reality. In fact, the only “element of reality”, while the rest is all subjective.

I invite you to have a look at my essay

regarding the role of “elements of reality” that we grant to mathematical entities like numbers and what are the consequences for natural sciences.

Very high rate from me, and good luck with the contest!

Flavio

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Let me add something to your sentence: “The Born rule [76], a fundamental component of Copenhagen interpretation, provides a link between mathematics and experimental observations.” . I would like to point out to you that the interpretation known as QBsim, whose author explicitly consider a refinement of Copenhagen, takes the Born rule as an element of reality. In fact, the only “element of reality”, while the rest is all subjective.

I invite you to have a look at my essay

regarding the role of “elements of reality” that we grant to mathematical entities like numbers and what are the consequences for natural sciences.

Very high rate from me, and good luck with the contest!

Flavio

report post as inappropriate

Dear Roman,

Your extremely important essay makes it possible to conclude: the centenary problem of the “foundations of mathematics” (justification, substantiation), which Morris Kline beautifully presented in “Mathematics: Loss of Certainty,” remains the philosophical and mathematical problem No. 1 for cognition as a whole. Uncertainty in the foundations of knowledge, the "language...

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Your extremely important essay makes it possible to conclude: the centenary problem of the “foundations of mathematics” (justification, substantiation), which Morris Kline beautifully presented in “Mathematics: Loss of Certainty,” remains the philosophical and mathematical problem No. 1 for cognition as a whole. Uncertainty in the foundations of knowledge, the "language...

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report post as inappropriate

Dear Vladimir,

Thank you for your kind words and for sharing some interesting references. I will be sure to read them. As to your last question, recent work by Wolfram may be an interesting direction to follow in that regard: https://www.wolframphysics.org/

Best,

Roman

Thank you for your kind words and for sharing some interesting references. I will be sure to read them. As to your last question, recent work by Wolfram may be an interesting direction to follow in that regard: https://www.wolframphysics.org/

Best,

Roman

Thank you very much, Roman, for your quick reply and link. I'm starting to read with interest.

Best,

Vladimir

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Best,

Vladimir

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hi roman I appreciate your comprehension of human observer.Do human selection effects filter into the eventual outcome of an experiment ,or vice versa.? please read/rate my take on my essay -https://fqxi.org/community/forum/topic/3525.i would greatly love to hear you on this topic. thanks and All the best to you

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Dear Roman,

Excellent Essay, please take a look at the long form version of my essay;

The sections where I compare biological complexity to computer, you will find that part very interesting

Please take a look at my essay A grand Introduction to Darwinian mechanic

https://fqxi.org/community/forum/topic/3549

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Excellent Essay, please take a look at the long form version of my essay;

The sections where I compare biological complexity to computer, you will find that part very interesting

Please take a look at my essay A grand Introduction to Darwinian mechanic

https://fqxi.org/community/forum/topic/3549

report post as inappropriate

We carefully read and discussed everything. There is something to think about. The scientific perspective is visible. Your ideas are very close to us! One of us works at the department of philosophy, the other at the department of computer science. Therefore, your essay was interesting to both of us. We really liked the use of the principle of "regression to infinity" for an observer in physics and for checking evidence in mathematics. This comparison is very heuristic. We liked the fact that you do not come to agnosticism. We believe in the possibilities of reason. But we think your approach has overtaken time. While in science there is not even a recognition of the objectivity of information. Therefore, ideas of this type are perceived as metaphors.

Now we are implementing a startup project to develop a fundamental ontology for integrating various ontologies of subject areas. We are creating a digital platform for this integration. Perhaps we can even establish mutually beneficial cooperation with you.

We hope you find our essay interesting.

Truly yours,

Pavel Poluian and Dmitry Lichargin,

Siberian Federal University.

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Now we are implementing a startup project to develop a fundamental ontology for integrating various ontologies of subject areas. We are creating a digital platform for this integration. Perhaps we can even establish mutually beneficial cooperation with you.

We hope you find our essay interesting.

Truly yours,

Pavel Poluian and Dmitry Lichargin,

Siberian Federal University.

report post as inappropriate

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