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**Steven Andresen**: *on* 2/22/18 at 8:49am UTC, wrote Dear Olaf If you are looking for another essay to read and rate in the...

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FQXi FORUM

January 27, 2020

CATEGORY:
FQXi Essay Contest - Spring, 2017
[back]

TOPIC: Physics and its a pre-Gödelian mindset by Olaf Dreyer [refresh]

TOPIC: Physics and its a pre-Gödelian mindset by Olaf Dreyer [refresh]

The goal of physics has always been to find the fundamental constituents of nature and their interactions. Once those are known the rest is nothing more than an application of this theory. This search for a fundamental theory is very much like Hilbert's goal to find the formal axiomatic system that describes all of mathematics. I argue that just like Hilbert's dream this one is equally doomed. It is the emergent phenomena that are to fundamental physics what true and unprovable statements are to mathematics. I show that there any number of such statements in physics and I provide an easy example. I further argue that emergence should not be seen as a weakness of physics. Rather, it is a way to obtain new insights into old problems.

I have obtained my PhD from the Pennsylvania State University while working on classical and quantum aspects of gravity. I continued my work in quantum gravity at the Perimeter Institute, Imperial College, MIT, & La Sapienza. I am now working as s consultant in finance.

Dear Olaf,

I appreciated your essay very much, thank you for sharing.

> In this essay we argue that emergent phenomena are to the laws of physics what true but unprovable statements are to formal axiomatic systems

A neat and powerful concept, well expressed even for not-physicist people like me. I agree with your idea – in my essay, being my formation philosophical, I touched similar arguments about sensations and consciousness (that's in your fig.2), and I tried to sketch a philosophical frame for emergence.

All the best, I wish you luck!

Francesco D'Isa

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I appreciated your essay very much, thank you for sharing.

> In this essay we argue that emergent phenomena are to the laws of physics what true but unprovable statements are to formal axiomatic systems

A neat and powerful concept, well expressed even for not-physicist people like me. I agree with your idea – in my essay, being my formation philosophical, I touched similar arguments about sensations and consciousness (that's in your fig.2), and I tried to sketch a philosophical frame for emergence.

All the best, I wish you luck!

Francesco D'Isa

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Dear Olaf,

I was curious about your essay, because it touches topics that are similar to the ones I first thought of, when I learned about this contest - my essay has not been posted yet, I hope it appears in the near future. I enjoyed the read, you write in a clear and fluent style.

I have a question. If I get you right, the main cause why a fundamental physical theory formulated in terms of position and momenta cannot assess the truth value of the statement “solid A touches solid B” is basically a problem of language. Is that right? The statement “solid A touches solid B” is not a statement about position and momenta, so the theory cannot determine whether it is true or false.

Gödel’s theorem, however, is not a problem of language. Gödel’s theorem states that any complex formal system contains statements with undecidable truth value, but those statements are formulated in exactly the language of the formal system. They are well-formed strings, they are meaningful within the language spoken by the formal system, and still, they can neither be proved true nor false.

In your example, were we to take the trouble to re-formulate the statement “solid A touches solid B” using the language of a physical theory based on positions and momenta (for example: “there is at least one atom in solid A whose distance to at least one atom of solid B is less than such-and-such a length”), then the theory would be able to decide whether the statement is true or false.

This, of course, does not prove you wrong. I do agree with the fact that emergence gives rise to phenomena that make sense at a higher level. But I wonder whether one can really draw a parallel with the incompleteness theorem. Am I interpreting things correctly?

Thanks for the read, it was a pleasure!

Inés.

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I was curious about your essay, because it touches topics that are similar to the ones I first thought of, when I learned about this contest - my essay has not been posted yet, I hope it appears in the near future. I enjoyed the read, you write in a clear and fluent style.

I have a question. If I get you right, the main cause why a fundamental physical theory formulated in terms of position and momenta cannot assess the truth value of the statement “solid A touches solid B” is basically a problem of language. Is that right? The statement “solid A touches solid B” is not a statement about position and momenta, so the theory cannot determine whether it is true or false.

Gödel’s theorem, however, is not a problem of language. Gödel’s theorem states that any complex formal system contains statements with undecidable truth value, but those statements are formulated in exactly the language of the formal system. They are well-formed strings, they are meaningful within the language spoken by the formal system, and still, they can neither be proved true nor false.

In your example, were we to take the trouble to re-formulate the statement “solid A touches solid B” using the language of a physical theory based on positions and momenta (for example: “there is at least one atom in solid A whose distance to at least one atom of solid B is less than such-and-such a length”), then the theory would be able to decide whether the statement is true or false.

This, of course, does not prove you wrong. I do agree with the fact that emergence gives rise to phenomena that make sense at a higher level. But I wonder whether one can really draw a parallel with the incompleteness theorem. Am I interpreting things correctly?

Thanks for the read, it was a pleasure!

Inés.

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Dear Ines,

thanks for reading and commenting! It took me some time to reply because I wanted to read your essay first (more on that in your thread). I see that you have been thinking along similar lines! I am not sure I understand your language remark so let me try make a couple more remarks about why I thing the analogy between incompleteness and emergence is apt:

If you have formal axiomatic system FAS_n and a true and unprovable statement you can add it to FAS_n and obtain a new FAS_(n+1). This new system will have its own true but unprovable statements which in turn can be added to the system to obtain FAS_(n+2) and so forth. You thus obtain a tower of theories (see image). This is much like the tower you obtain from emergence. Statements about the solids in my example are added to the statements about atoms to form a new theory. Note that this addition is not arbitrary. It is important that the solid is made of atoms and thus that the new set of statements remains consistent.

You propose the sentence „there is at least one atom in solid A …“ which is a reformulation of my shorter statement. Note, though, that you need to know about solids to make this statement. What is a solid? All you have is a (long) list of positions and momenta. Finding the solids is the hardest part. It only looks easy because we note the positions and momenta using coordinates that come from the solids themselves.

Thanks again for reading!

Cheers

Olaf

thanks for reading and commenting! It took me some time to reply because I wanted to read your essay first (more on that in your thread). I see that you have been thinking along similar lines! I am not sure I understand your language remark so let me try make a couple more remarks about why I thing the analogy between incompleteness and emergence is apt:

If you have formal axiomatic system FAS_n and a true and unprovable statement you can add it to FAS_n and obtain a new FAS_(n+1). This new system will have its own true but unprovable statements which in turn can be added to the system to obtain FAS_(n+2) and so forth. You thus obtain a tower of theories (see image). This is much like the tower you obtain from emergence. Statements about the solids in my example are added to the statements about atoms to form a new theory. Note that this addition is not arbitrary. It is important that the solid is made of atoms and thus that the new set of statements remains consistent.

You propose the sentence „there is at least one atom in solid A …“ which is a reformulation of my shorter statement. Note, though, that you need to know about solids to make this statement. What is a solid? All you have is a (long) list of positions and momenta. Finding the solids is the hardest part. It only looks easy because we note the positions and momenta using coordinates that come from the solids themselves.

Thanks again for reading!

Cheers

Olaf

Hi, Olaf, thanks for your reply! Yes, we took the topic of the contest along the same lines, that's good, it means there must be something there! I think I fully agree with all what you say, my comment about the language thing is just a matter of what to stress.

> Note, though, that you need to know about solids to make this statement. What is a solid? All you have is a (long) list of positions and momenta. Finding the solids is the hardest part.

Precisely! In your example the obstacle is the definition of a solid in terms of microscopic variables. Being a definition, I referred to the problem as a matter of language. The theory is written in the language of position and momenta, but the statement is stated in the macroscopic language of large objects. There is an incompatibility between the two languages, and that is why the microscopic theory cannot assess the truth value of the macroscopic statement. Gödel's theorem, however, is not a matter of language. The unprovability of some statements is present even for statements that are written in exactly the same language as the one of the theory. In a way, Gödel identified an even more serious problem, because his unprovability is still there in the absence of translation problems.

But never mind this, it does not challenge your main emergence conclusion. Because in addition to Gödel's unprovability, we also have to deal with the scale/language/emergence un-assessability you discuss.

Best!

inés.

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> Note, though, that you need to know about solids to make this statement. What is a solid? All you have is a (long) list of positions and momenta. Finding the solids is the hardest part.

Precisely! In your example the obstacle is the definition of a solid in terms of microscopic variables. Being a definition, I referred to the problem as a matter of language. The theory is written in the language of position and momenta, but the statement is stated in the macroscopic language of large objects. There is an incompatibility between the two languages, and that is why the microscopic theory cannot assess the truth value of the macroscopic statement. Gödel's theorem, however, is not a matter of language. The unprovability of some statements is present even for statements that are written in exactly the same language as the one of the theory. In a way, Gödel identified an even more serious problem, because his unprovability is still there in the absence of translation problems.

But never mind this, it does not challenge your main emergence conclusion. Because in addition to Gödel's unprovability, we also have to deal with the scale/language/emergence un-assessability you discuss.

Best!

inés.

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Cool. I am in the midst of reading *Exact Thinking in Demented Times: The Vienna Circle*. Gödel and Hilbert are mentioned often.

Question: how deep could any undecidable-like character of physics go? In particular, it is hard to imagine (maybe not impossible) that a fundamental particle might exist without there being any way to prove that it does. Quarks are not observable in any ordinary sense, but they are inferrable, which is proof enough. If there is any kind of interaction with ordinary matter, then existence could be inferred. Anyway, just thinking.

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Question: how deep could any undecidable-like character of physics go? In particular, it is hard to imagine (maybe not impossible) that a fundamental particle might exist without there being any way to prove that it does. Quarks are not observable in any ordinary sense, but they are inferrable, which is proof enough. If there is any kind of interaction with ordinary matter, then existence could be inferred. Anyway, just thinking.

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Dear Geoffrey,

thank you for reading and commenting!

I think you are right. If there were a particle that is fundamental but we can not know about it then we do not really care about it. It would exist in a world that is disjunct from ours. Only if the particle had some effect would we care about it but then we would also be able to investigate those effects.

Cheers

Olaf

thank you for reading and commenting!

I think you are right. If there were a particle that is fundamental but we can not know about it then we do not really care about it. It would exist in a world that is disjunct from ours. Only if the particle had some effect would we care about it but then we would also be able to investigate those effects.

Cheers

Olaf

Greetings:

I think you have shown that truth in physics is insufficient to evaluate a physics model's usefulness to humanity. A different scheme is necessary to determine the physics models to pursue.

"Touches" is a definition problem. Does the Earth "touch" the moon (they do appear to influence each other).

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I think you have shown that truth in physics is insufficient to evaluate a physics model's usefulness to humanity. A different scheme is necessary to determine the physics models to pursue.

"Touches" is a definition problem. Does the Earth "touch" the moon (they do appear to influence each other).

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Dear John,

thank you for the interest in my essay!

You are right to point out that touches is a bit vague. I just needed any statement involving the two solids. Any statement would do. Any ideas?

Cheers

O.

thank you for the interest in my essay!

You are right to point out that touches is a bit vague. I just needed any statement involving the two solids. Any statement would do. Any ideas?

Cheers

O.

"influences" ,but then everything "touches" everything else to varying degrees. This is the problem. So, the mechanism of "touching" should be one of the fundamentals.

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Hi Olaf,

I exaggerate to no degree when I say that yours is a truly brilliant essay. I love the way in which you spoke of Gödel's theorem, and the brilliant manner in which emergence emerged (har, har, har). I completely agree with your point of view; not all things are quantifiable.

However, much like Gödel's theorem, this result majorly leaves one's sense of aesthetics rather unsatisfied. And so, although I myself abandoned formal analysis, I did go forth and attempt to tackle the issue in another manner which I feel is not susceptible to the feared theorem-it might be of interest you.

Regards,

Aditya

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I exaggerate to no degree when I say that yours is a truly brilliant essay. I love the way in which you spoke of Gödel's theorem, and the brilliant manner in which emergence emerged (har, har, har). I completely agree with your point of view; not all things are quantifiable.

However, much like Gödel's theorem, this result majorly leaves one's sense of aesthetics rather unsatisfied. And so, although I myself abandoned formal analysis, I did go forth and attempt to tackle the issue in another manner which I feel is not susceptible to the feared theorem-it might be of interest you.

Regards,

Aditya

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Dear DR Olaf Dreyer,

Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

Joe Fisher, Realist

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Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

Joe Fisher, Realist

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Dear Olaf,

I've elsewhere remarked on how these essay contests seem to bring certain common strands of thought to the fore---so I'm happy to see another essay using a Gödelian analogy to argue against the possibility of having an overarching framework accounting for all of the world (or at least, all of physics). I think (and argue in my own essay, if you'll excuse the advertisement) that scientists will have to learn the lesson that mathematicians have learned almost 90 years ago---that it does not mean an end to our efforts if they can't be unified in a single axiomatic system.

However, I'm not sure I really understand your example of a physical 'Gödel-sentence'. It seems to me that if you were to input the description of your system into a sufficiently powerful computer, it could run a simulation by means of which it would indeed conclude that the tow solids touch---thus, the truth of the proposition is decidable from the axioms after all.

Or did you have something else in mind?

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I've elsewhere remarked on how these essay contests seem to bring certain common strands of thought to the fore---so I'm happy to see another essay using a Gödelian analogy to argue against the possibility of having an overarching framework accounting for all of the world (or at least, all of physics). I think (and argue in my own essay, if you'll excuse the advertisement) that scientists will have to learn the lesson that mathematicians have learned almost 90 years ago---that it does not mean an end to our efforts if they can't be unified in a single axiomatic system.

However, I'm not sure I really understand your example of a physical 'Gödel-sentence'. It seems to me that if you were to input the description of your system into a sufficiently powerful computer, it could run a simulation by means of which it would indeed conclude that the tow solids touch---thus, the truth of the proposition is decidable from the axioms after all.

Or did you have something else in mind?

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Hi Jochen,

thanks for your comment! You are making an important point that I tried (and obviously failed) to address properly in the essay. Let me try again.

If you have the list of positions and momenta you will be able to find the solids (how would you actually do it? Not knowing the distances in the solid I would write a Fourier transform of the data and look for the peaks. These give you the distances. Then you just need to sort …). The important point here is that you already know what you are looking for! It is especially easy because the way you write down the positions and momenta will be in a basis that is constructed from the solids themselves. You measure space by taking the solids and putting one next to the other. This is the reason why the program you want to write is so simple.

Now imagine I don’t give you the particles in such nice coordinates. I could use a function that is arbitrarily complex to represent the positions and momenta so that you would not be able to discover the order (even if you knew what you where looking for). This is in fact the situation that you face in solid state physics all the time. You can write down the Hamiltonian and you know the phenomena that you want to describe but you have no way of getting from one to the other. It is the rigidity of the solids that is invariant under such transformations. The solids will push back when pushed and doesn’t care about the way you represent the atoms.

Thanks again for reading.

Cheers

Olaf

thanks for your comment! You are making an important point that I tried (and obviously failed) to address properly in the essay. Let me try again.

If you have the list of positions and momenta you will be able to find the solids (how would you actually do it? Not knowing the distances in the solid I would write a Fourier transform of the data and look for the peaks. These give you the distances. Then you just need to sort …). The important point here is that you already know what you are looking for! It is especially easy because the way you write down the positions and momenta will be in a basis that is constructed from the solids themselves. You measure space by taking the solids and putting one next to the other. This is the reason why the program you want to write is so simple.

Now imagine I don’t give you the particles in such nice coordinates. I could use a function that is arbitrarily complex to represent the positions and momenta so that you would not be able to discover the order (even if you knew what you where looking for). This is in fact the situation that you face in solid state physics all the time. You can write down the Hamiltonian and you know the phenomena that you want to describe but you have no way of getting from one to the other. It is the rigidity of the solids that is invariant under such transformations. The solids will push back when pushed and doesn’t care about the way you represent the atoms.

Thanks again for reading.

Cheers

Olaf

Dar Olaf,

I bare bruises for suggesting that physics has some Turing machine/Godel type of incompleteness. I suppose the idea seems to be percolating out into the world.

I think the quantum classical dichotomy is a case of this. The measurement of a quantum system couples that system with a reservoir of states. The quantum system then becomes entangled with this reservoir of states as superpositions and entanglements in that system are reduced. This all sounds unsurprising, as this is just decoherence. However, in the case of an emergent classical state, say the needle of an instrument or a general classical configuration, we lack the quantum mechanical tools necessary to understand this. Quantum mechanics is basis independent and we are demanding that it somehow produce a prediction for a fixed classical basis. I see this as a possible instance of Godel incompleteness with self-referential qubits.

Cheers LC

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I bare bruises for suggesting that physics has some Turing machine/Godel type of incompleteness. I suppose the idea seems to be percolating out into the world.

I think the quantum classical dichotomy is a case of this. The measurement of a quantum system couples that system with a reservoir of states. The quantum system then becomes entangled with this reservoir of states as superpositions and entanglements in that system are reduced. This all sounds unsurprising, as this is just decoherence. However, in the case of an emergent classical state, say the needle of an instrument or a general classical configuration, we lack the quantum mechanical tools necessary to understand this. Quantum mechanics is basis independent and we are demanding that it somehow produce a prediction for a fixed classical basis. I see this as a possible instance of Godel incompleteness with self-referential qubits.

Cheers LC

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Dear Lawrence,

thanks for reading and replying!

I completely agree with you. I also think that the classical/quantum problem is an example of what I am trying to say. The last picture in the essay contains a bubble saying QM & Classicality (

). That is what I mean by that.

You mention the point about the basis independence of quantum mechanics. I was thinking that this is related to the point I made in the section*Seizing Gödel*. Generalized rigidity creates a particular basis. In my example it is the the basis given by the solids. So the choice of basis is a dynamic effect.

What do you think?

Cheers

Olaf

thanks for reading and replying!

I completely agree with you. I also think that the classical/quantum problem is an example of what I am trying to say. The last picture in the essay contains a bubble saying QM & Classicality (

Emergence is central to a number of problems. QM among them. |

You mention the point about the basis independence of quantum mechanics. I was thinking that this is related to the point I made in the section

What do you think?

Cheers

Olaf

I was intending to respond with a longer discussion. I will have to postpone that until later. I will say that I think an aspect of the quantum measurement problem as an undecidable proposition is related to an aspect of quantum gravitation. If you read my essay you find I propose a duality between the unitarity and equivalence principles of quantum mechanics and general relativity. This in a quantum context leads to a sort of paradox of the same nature as the quantum measurement issue.

I will return to this in the near future. It got late today and I will probably write a better discussion tomorrow.

Cheers LC

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I will return to this in the near future. It got late today and I will probably write a better discussion tomorrow.

Cheers LC

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To continue onwards with what I started, I thought I would break this out some with regards to quantum gravitation.

With the measurement issue a quantum system with some set of states, usually rather small in number or with a few number of degrees of freedom, by a classical-like system. By the use of “like” it is a reference to the fact this system is really in fact quantum mechanical....

view entire post

With the measurement issue a quantum system with some set of states, usually rather small in number or with a few number of degrees of freedom, by a classical-like system. By the use of “like” it is a reference to the fact this system is really in fact quantum mechanical....

view entire post

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Dear Olaf,

Nice Essay, connected with the fundamental question of physics: “Does the fundamental theory of nature exist?” You argue, making an intriguing parallelism with Gödelian incompleteness, that the answer should be “no”. Despite I agree with your statement that “To exclusively look for the fundamental theory of nature is as narrow a search as the search for the formal axiomatic system that underlies mathematics”, I must add that this does not automatically imply that such a fundamental theory of nature does not exist. Einstein's position on this issue was of substantial uncertainty. We all recall his quest for a unified field theory in the latest years of his life. On the other hand, he aslo claimed that it should not exist a fundamental theory of nature but only subsequent theories which explain nature with always increasing approximation levels. I am substantially incerte in the same way.

Finally, I completely agree with your point that emergence is not a weakness of physics (despite I have various dubts on energent gravity), but it could be a useful tool instead.

In any case, I find your Essay to be entertaining and intriguing. Thus, it deserves my high score.

As I know that you are an expert on black hole quasi-normal modes (despite I am astonished that you are now working as consultant in finance), maybe you could be interested in my Essay, where I discuss about them (and also on the unified field theory) ... with Albert Einstein!

Good luck in the Contest.

Cheers, Ch.

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Nice Essay, connected with the fundamental question of physics: “Does the fundamental theory of nature exist?” You argue, making an intriguing parallelism with Gödelian incompleteness, that the answer should be “no”. Despite I agree with your statement that “To exclusively look for the fundamental theory of nature is as narrow a search as the search for the formal axiomatic system that underlies mathematics”, I must add that this does not automatically imply that such a fundamental theory of nature does not exist. Einstein's position on this issue was of substantial uncertainty. We all recall his quest for a unified field theory in the latest years of his life. On the other hand, he aslo claimed that it should not exist a fundamental theory of nature but only subsequent theories which explain nature with always increasing approximation levels. I am substantially incerte in the same way.

Finally, I completely agree with your point that emergence is not a weakness of physics (despite I have various dubts on energent gravity), but it could be a useful tool instead.

In any case, I find your Essay to be entertaining and intriguing. Thus, it deserves my high score.

As I know that you are an expert on black hole quasi-normal modes (despite I am astonished that you are now working as consultant in finance), maybe you could be interested in my Essay, where I discuss about them (and also on the unified field theory) ... with Albert Einstein!

Good luck in the Contest.

Cheers, Ch.

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Dear Christian,

Thanks so much for reading my essay and taking the time to reply.

I totally agree with your comment that "this does not automatically imply that such a fundamental theory of nature does not exist." All I wanted to say was that even if we had such a fundamental theory we would not be able to answer all the interesting questions.

I am looking forward to reading your essay! Quasi-normal modes and A. Einstein himself. Who can say no to that!?

About the finance thing: sometimes life doesn't work out as planned...

Talk to you in your thread.

Cheers

Olaf

Thanks so much for reading my essay and taking the time to reply.

I totally agree with your comment that "this does not automatically imply that such a fundamental theory of nature does not exist." All I wanted to say was that even if we had such a fundamental theory we would not be able to answer all the interesting questions.

I am looking forward to reading your essay! Quasi-normal modes and A. Einstein himself. Who can say no to that!?

About the finance thing: sometimes life doesn't work out as planned...

Talk to you in your thread.

Cheers

Olaf

Dear Olaf,

once more an essay with Gödel’s results involved. And I like it. But I also have some suspicions.

If I take your analogy serious, I conclude that you have proven consciousness to be an emergent phenomenon. Since consciousness is needed to at all be aware of something like ‘emergence’ and consciousness in your framework is an emergent property of reality, it follows...

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once more an essay with Gödel’s results involved. And I like it. But I also have some suspicions.

If I take your analogy serious, I conclude that you have proven consciousness to be an emergent phenomenon. Since consciousness is needed to at all be aware of something like ‘emergence’ and consciousness in your framework is an emergent property of reality, it follows...

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Dear Stefan,

thank you for reading and commenting!

Since you brought up consciousness I should probably say something about it. I think it is true that emergence has a role to play in our understanding of consciousness. It is not enough, though, to just claim that consciousness is emergent. One has to do better than that. I give one hint about what I am thinking in the section*Seizing Gödel*. Because of generalized rigidity there is meaning to the solids, namely their positions. The important point is that the meaning is internal to the solids. Just push them and you know where they are. This is an important first step to breaking the infinite regress that plagues the consciousness debate: you always seem to need an external observer. To understand the meaning of a solid you do not need anything other than another solid. The big question now becomes: what about the "I". Where does that come from? I have some ideas about that but they'll have to wait for another essay ...

About your question concerning the ladder of emergence. The real answer is that we can not be sure of course. There is no certainty in either direction. What is likely though is that for our relationship with nature only a handful of layers will be important.

Thanks again!

Cheers

Olaf

thank you for reading and commenting!

Since you brought up consciousness I should probably say something about it. I think it is true that emergence has a role to play in our understanding of consciousness. It is not enough, though, to just claim that consciousness is emergent. One has to do better than that. I give one hint about what I am thinking in the section

About your question concerning the ladder of emergence. The real answer is that we can not be sure of course. There is no certainty in either direction. What is likely though is that for our relationship with nature only a handful of layers will be important.

Thanks again!

Cheers

Olaf

Hi Olaf,

thanks so much for your reply. Emergence is not a bad idea, i think, albeit i have the impression that it freely levitates between the assumption of nature being fully formalizable and nature being only formalizable to a certain degree due to in-principle reasons (due to some fundamentals we yet don't know for sure).

I would be eager to read your next essay!

Good luck,

Stefan Weckbach

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thanks so much for your reply. Emergence is not a bad idea, i think, albeit i have the impression that it freely levitates between the assumption of nature being fully formalizable and nature being only formalizable to a certain degree due to in-principle reasons (due to some fundamentals we yet don't know for sure).

I would be eager to read your next essay!

Good luck,

Stefan Weckbach

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Oh, i have an essay too in the contest. I would be happy if you would like to read and comment on it Olaf. Maybe what i describe is not so far apart from your concept of emergence?

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Dear Olaf,

thank you for sharing this nice essay, that I enjoyed very much reading.

Although from a very different perspective,you will find similar position in my essay. For instance, the failure of some naive fundamental research programs, like the one of a complete axiomatization of physics.

All good wishes,

Flavio

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thank you for sharing this nice essay, that I enjoyed very much reading.

Although from a very different perspective,you will find similar position in my essay. For instance, the failure of some naive fundamental research programs, like the one of a complete axiomatization of physics.

All good wishes,

Flavio

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dear Olaf,

I am glad that I read your essay because in my mind you were always about collapse.. and all from reading a lot about your past research, which was like beating a skeleton of a horse. I was surprised to hear you talking along the lines of my thinking. which I write

"Now suppose I ask you to tell me what will happen to some "object", but I don't tell you anything about it (how fundamental can you get) !! like what mass it has or what it will do if another thing is present. Ok, I'll give it a try. First I will say I will "invent a coordinate and since I don't know where it exists I will restrict it to be in some range and eventually make that range variable. This lonely thing would have a meaningless existence. i.e. it needs a partner. If we add another one next to it with similar setup and at some distance that can also be varied. Now, we can calculate all relative information just like our original idea in the essay.

Kaboom! both situations reached the same conclusion with generalization leading to all (at least important parts up to now) of physics QM, QFT, Gravity like shown. In one instance we acted like GOD and decided to design a dynamic universe, in the other we are ignorant humans but figured out how things should work, and both match and are the FUNDAMENTAL building block. "

I hope you can glance at my essay and tell me if it makes any sense. Thanks

https://fqxi.org/community/forum/topic/3127

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I am glad that I read your essay because in my mind you were always about collapse.. and all from reading a lot about your past research, which was like beating a skeleton of a horse. I was surprised to hear you talking along the lines of my thinking. which I write

"Now suppose I ask you to tell me what will happen to some "object", but I don't tell you anything about it (how fundamental can you get) !! like what mass it has or what it will do if another thing is present. Ok, I'll give it a try. First I will say I will "invent a coordinate and since I don't know where it exists I will restrict it to be in some range and eventually make that range variable. This lonely thing would have a meaningless existence. i.e. it needs a partner. If we add another one next to it with similar setup and at some distance that can also be varied. Now, we can calculate all relative information just like our original idea in the essay.

Kaboom! both situations reached the same conclusion with generalization leading to all (at least important parts up to now) of physics QM, QFT, Gravity like shown. In one instance we acted like GOD and decided to design a dynamic universe, in the other we are ignorant humans but figured out how things should work, and both match and are the FUNDAMENTAL building block. "

I hope you can glance at my essay and tell me if it makes any sense. Thanks

https://fqxi.org/community/forum/topic/3127

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Let me add one clarification.

As a matter of fact you don't need the coordinate, you can derive it by the NUMBERS that you have started with originally. And of course the numbers themselves are unimportant, only their relative values.Hence the pun on Pythagoreans declaration ALL is number.

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As a matter of fact you don't need the coordinate, you can derive it by the NUMBERS that you have started with originally. And of course the numbers themselves are unimportant, only their relative values.Hence the pun on Pythagoreans declaration ALL is number.

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Olaf fabulous essay. I have rated it very highly.

What if we could draw actual axioms for example "the definition of the imaginary unit" as a drawing element on a geometry, then we could instantly see how that relates to "complex numbers" which don't use the actual definitional imaginary unit. That is, the definition of i is very different from the "i" used in the complex numbers z=a+ib since the definitional i is alone as a "drawing element" while all the z's use only a constricted "i" enveloped with the "real numbers" a and b. In this scenario we could see if the definitional i causes the "emergence" of the "complex numbers".

I took the completely opposite route to you -- I devised a "new maths" that avoids Godel's work by looking at totalities. It basically is "a physics of complex numbers", we show that complex numbers "parts" (the real part and the imaginary parts) are due to momogamy the pure qm property of how the system and it sub-systems interact. If you some time then see my essay What is fundamental is the area of the imaginary unit" for more details. Please read the FAQ attachment on the first post.

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What if we could draw actual axioms for example "the definition of the imaginary unit" as a drawing element on a geometry, then we could instantly see how that relates to "complex numbers" which don't use the actual definitional imaginary unit. That is, the definition of i is very different from the "i" used in the complex numbers z=a+ib since the definitional i is alone as a "drawing element" while all the z's use only a constricted "i" enveloped with the "real numbers" a and b. In this scenario we could see if the definitional i causes the "emergence" of the "complex numbers".

I took the completely opposite route to you -- I devised a "new maths" that avoids Godel's work by looking at totalities. It basically is "a physics of complex numbers", we show that complex numbers "parts" (the real part and the imaginary parts) are due to momogamy the pure qm property of how the system and it sub-systems interact. If you some time then see my essay What is fundamental is the area of the imaginary unit" for more details. Please read the FAQ attachment on the first post.

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Olaf,

Very good essay. One of the few I'd have really liked to see longer, though you argued the case well and not to concisely. Nicely written and I also agreed with just about all. I do like to 'look at old problems in new ways'.

Perhap's you could comment on an interesting proposition, not so much from this year but my 2015 'Red/Green Sock Trick' essay. I suggest a common underlying structure simply following the rules of brackets in arithmetic, which is also as modal / 'quantum' logic. Infinitely many functions within functions or spaces within spaces in motion can exist but only have direct relationships with the next one up. They carry on down with Godel (who I agree is dismissed along with agony aunt Marilyn Savant who I'm sure you're familiar with!).

Accompanying that is the Law of The Reducing Middle' No problematic binary 'excluded middle' but a Bayesian distribution of possibilities. Then perhaps read this years essay to evaluate it's power!

Great job on yours, right on topic and lovely style. Top Marks.

Very best.

Peter

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Very good essay. One of the few I'd have really liked to see longer, though you argued the case well and not to concisely. Nicely written and I also agreed with just about all. I do like to 'look at old problems in new ways'.

Perhap's you could comment on an interesting proposition, not so much from this year but my 2015 'Red/Green Sock Trick' essay. I suggest a common underlying structure simply following the rules of brackets in arithmetic, which is also as modal / 'quantum' logic. Infinitely many functions within functions or spaces within spaces in motion can exist but only have direct relationships with the next one up. They carry on down with Godel (who I agree is dismissed along with agony aunt Marilyn Savant who I'm sure you're familiar with!).

Accompanying that is the Law of The Reducing Middle' No problematic binary 'excluded middle' but a Bayesian distribution of possibilities. Then perhaps read this years essay to evaluate it's power!

Great job on yours, right on topic and lovely style. Top Marks.

Very best.

Peter

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Hi Olaf,

Your idea of emergence is at the center of the physics is very beautiful...which is including consciousness and incompleteness... Very good...

Here in my essay energy to mass conversion is proposed...……..….. yours is very nice essay best wishes …. I highly appreciate hope your essay and hope for reciprocity ….You may please spend some of the valuable time on...

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Your idea of emergence is at the center of the physics is very beautiful...which is including consciousness and incompleteness... Very good...

Here in my essay energy to mass conversion is proposed...……..….. yours is very nice essay best wishes …. I highly appreciate hope your essay and hope for reciprocity ….You may please spend some of the valuable time on...

view entire post

post approved

Dear Olaf Dreyer

Just letting you know that I am making a start on reading of your essay, and hope that you might also take a glance over mine please? I look forward to the sharing of thoughtful opinion. Congratulations on your essay rating as it stands, and best of luck for the contest conclusion.

My essay is titled

“Darwinian Universal Fundamental Origin”. It stands as a novel test for whether a natural organisational principle can serve a rationale, for emergence of complex systems of physics and cosmology. I will be interested to have my effort judged on both the basis of prospect and of novelty.

Thank you & kind regards

Steven Andresen

post approved

Just letting you know that I am making a start on reading of your essay, and hope that you might also take a glance over mine please? I look forward to the sharing of thoughtful opinion. Congratulations on your essay rating as it stands, and best of luck for the contest conclusion.

My essay is titled

“Darwinian Universal Fundamental Origin”. It stands as a novel test for whether a natural organisational principle can serve a rationale, for emergence of complex systems of physics and cosmology. I will be interested to have my effort judged on both the basis of prospect and of novelty.

Thank you & kind regards

Steven Andresen

post approved

Dear Olaf,

I have enjoyed reading your concise and to the point essay. Just wondering whether I got it right that you use 'emergence' not in the naturalistic (bottom up), but rather in the sense of 'spontaneous idea' implying human agency.

Heinrich

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I have enjoyed reading your concise and to the point essay. Just wondering whether I got it right that you use 'emergence' not in the naturalistic (bottom up), but rather in the sense of 'spontaneous idea' implying human agency.

Heinrich

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Dear Olaf,

Thank you for a very nice essay. Godel's theorem is indeed very deep.

One must also look at Turing's halting theorem. You might also look at the

following book which deals with such issues "Computability in Analysis and Physics"

Please take a look at my essay.

Thank you again for a very readable essay.

All the best,

Noson Yanofsky

By Marian B. Pour-El, J. Ian Richards

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Thank you for a very nice essay. Godel's theorem is indeed very deep.

One must also look at Turing's halting theorem. You might also look at the

following book which deals with such issues "Computability in Analysis and Physics"

Please take a look at my essay.

Thank you again for a very readable essay.

All the best,

Noson Yanofsky

By Marian B. Pour-El, J. Ian Richards

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Dear Olaf,

Very nice essay, clear and deep message in a brief and well written form. I like your statement "emergent phenomena that are to fundamental physics what true and unprovable statements are to mathematics". In fact I wrote about incompleteness and limits of computability in relation to emergence and reductionism in my previous essay. In particular if you look at the figure in section 4 you may see how much we agree. Your example with solids touching is intriguingly simple, but at this point I don't understand why we can't prove they touch. If some of the positions in the list repeat, I think they touch, am I missing something? Also if they touch the dynamics will "know", because the evolution will include a collision. Perhaps the meaning is that the list of positions and momenta contain only positions and momenta, and the touching or collision can only be inferred from the list?

Best regards,

Cristi Stoica

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Very nice essay, clear and deep message in a brief and well written form. I like your statement "emergent phenomena that are to fundamental physics what true and unprovable statements are to mathematics". In fact I wrote about incompleteness and limits of computability in relation to emergence and reductionism in my previous essay. In particular if you look at the figure in section 4 you may see how much we agree. Your example with solids touching is intriguingly simple, but at this point I don't understand why we can't prove they touch. If some of the positions in the list repeat, I think they touch, am I missing something? Also if they touch the dynamics will "know", because the evolution will include a collision. Perhaps the meaning is that the list of positions and momenta contain only positions and momenta, and the touching or collision can only be inferred from the list?

Best regards,

Cristi Stoica

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Dear Olaf

If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don’t rate them at all. Infact I haven’t issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to...

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If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don’t rate them at all. Infact I haven’t issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to...

view entire post

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