If you are aware of an interesting new academic paper (that has been published in a peer-reviewed journal or has appeared on the arXiv), a conference talk (at an official professional scientific meeting), an external blog post (by a professional scientist) or a news item (in the mainstream news media), which you think might make an interesting topic for an FQXi blog post, then please contact us at forums@fqxi.org with a link to the original source and a sentence about why you think that the work is worthy of discussion. Please note that we receive many such suggestions and while we endeavour to respond to them, we may not be able to reply to all suggestions.

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Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

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Current Essay Contest

*Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation*

Media Partner: Scientific American

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*December 24, 2019 - April 24, 2020*

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

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*October 28, 2017 to January 22, 2018*

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

*December 2, 2016 to March 3, 2017*

Contest Partner: The Peter and Patricia Gruber Fund.

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**Trick or Truth: The Mysterious Connection Between Physics and Mathematics**

*Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation*

Media Partner: Scientific American

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*January 9, 2014 - August 31, 2014*

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*March 25 - June 28, 2013*

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**The Nature of Time**

*August - December 2008*

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Current Essay Contest

Media Partner: Scientific American

Previous Contests

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

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

Contest Partner: The Peter and Patricia Gruber Fund.

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RECENT POSTS IN THIS TOPIC

**Akinbo Ojo**: *on* 6/18/15 at 14:28pm UTC, wrote Hi Armin, Would you mind if I tapped your brain a little? I have a draft...

**Armin Nikkhah Shirazi**: *on* 4/23/15 at 17:41pm UTC, wrote Dear Bill, Thank you for your comments. I regret that you found the...

**William Parsons**: *on* 4/22/15 at 14:43pm UTC, wrote Hi Armin-- I have been remiss in not commenting on your essay. I...

**Torsten Asselmeyer-Maluga**: *on* 4/21/15 at 11:05am UTC, wrote Dear Armin, thanks for reading my essay and for the comment. You are...

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FQXi FORUM

August 12, 2022

CATEGORY:
Trick or Truth Essay Contest (2015)
[back]

TOPIC: Imagination and the Unreasonable Effectiveness of Mathematics by Armin Nikkhah Shirazi [refresh]

TOPIC: Imagination and the Unreasonable Effectiveness of Mathematics by Armin Nikkhah Shirazi [refresh]

At least since a famous 1960 paper by Wigner, the effectiveness of mathematics in the natural sciences has been the subject of ongoing debate. This paper argues that if we take nature to be consistent, then given that we have complete freedom short of inconsistency in choosing axioms to mathematically model reality, we \emph{should} expect mathematics to potentially be ``unreasonably'' effective in modeling reality. The reason why it actually turns out to be so, however, is attributable to human imagination.\\ As a case study to illustrate this, I present highlights of recent work which attempts to connect the foundations of mathematics to the foundations of quantum mechanics by means of a tentative novel axiom to be added to ZFC set theory. This axiom is meant to formally introduce into mathematics the intuitive distinction between actualities and potentialities by permitting the construction of novel mathematical objects which are in a certain sense incomplete. These objects exhibit quantum-like features, and a theorem directly connects them to the Feynman path integral for the simplest possible case.

See http://fqxi.org/community/forum/topic/2102

Hi Armin,

Good to see you again in the contest. Last time I did write a long reply to your critique of my theory but never got to post it, because I never finished it. But your questions which I knew about it already but you forced me to analyse lead to the greatest discovery in my system. The PROTON size. So thank you, thank you.

I will address all your other questions, and I emphasize that your theory is mine but you need to make just a bit different interpretation of what you have come up with.

I hope your programming skills have gotten a bit better. But don't worry, I have added the links to all the programs in JavaScript that are very easy. Look at all the new fantastic results, check them out or let a friend do it. Armin, my theory is very much yours but in disguise. You see the line that you take to go to infinity I just randomize it to all values, next, take two such lines representing two particles, cross the random lines in the manner of my program and Wala the whole god damn reality comes out. That is all there is to it. The same for the EPR, the same. More later.

Essay

Thanks and good luck.

report post as inappropriate

report post as inappropriate

Good to see you again in the contest. Last time I did write a long reply to your critique of my theory but never got to post it, because I never finished it. But your questions which I knew about it already but you forced me to analyse lead to the greatest discovery in my system. The PROTON size. So thank you, thank you.

I will address all your other questions, and I emphasize that your theory is mine but you need to make just a bit different interpretation of what you have come up with.

I hope your programming skills have gotten a bit better. But don't worry, I have added the links to all the programs in JavaScript that are very easy. Look at all the new fantastic results, check them out or let a friend do it. Armin, my theory is very much yours but in disguise. You see the line that you take to go to infinity I just randomize it to all values, next, take two such lines representing two particles, cross the random lines in the manner of my program and Wala the whole god damn reality comes out. That is all there is to it. The same for the EPR, the same. More later.

Essay

Thanks and good luck.

report post as inappropriate

Hi Adel,

Thank you for your comments. I vaguely remember some of my criticisms, the one which stands out most clearly in my mind was whether you could account for the fact that the wave function is a probability amplitude. During the last 1.5 years that I have been more focused on mathematics, I have noticed that some of that "thinking like a mathematician" has rubbed off on me, in the sense that I tend to now be a lot more careful with certain statements that would have seemed obvious to me before. I mention this because your assertion that "your theory is mine" strikes me as something which is not immediately obvious to me, especially because I do not recall that you made a formal distinction between actuality and potentiality, on which essentially my entire framework is based. However, I will read your essay and give you further feedback in the next few days.

Thanks again,

Armin

Thank you for your comments. I vaguely remember some of my criticisms, the one which stands out most clearly in my mind was whether you could account for the fact that the wave function is a probability amplitude. During the last 1.5 years that I have been more focused on mathematics, I have noticed that some of that "thinking like a mathematician" has rubbed off on me, in the sense that I tend to now be a lot more careful with certain statements that would have seemed obvious to me before. I mention this because your assertion that "your theory is mine" strikes me as something which is not immediately obvious to me, especially because I do not recall that you made a formal distinction between actuality and potentiality, on which essentially my entire framework is based. However, I will read your essay and give you further feedback in the next few days.

Thanks again,

Armin

Dear Armin,

I welcome the above summary of your work: 'Essentially my entire framework is based on a formal distinction between actuality and potentiality.' But I must think hard about it further. For, once throwing a dice in my sister's kitchen, her cat "perceived a mouse" and swallowed it mid-run!

Nevertheless, the above summary provides a sound basis for our agreeing with Bohr’s...

view entire post

I welcome the above summary of your work: 'Essentially my entire framework is based on a formal distinction between actuality and potentiality.' But I must think hard about it further. For, once throwing a dice in my sister's kitchen, her cat "perceived a mouse" and swallowed it mid-run!

Nevertheless, the above summary provides a sound basis for our agreeing with Bohr’s...

view entire post

report post as inappropriate

Armin, I've added this note here to facilitate continuity in our discussion:

Discussion on the above components of this thread continues here.

With best regards; Gordon Watson: Essay Forum. Essay Only.

report post as inappropriate

Discussion on the above components of this thread continues here.

With best regards; Gordon Watson: Essay Forum. Essay Only.

report post as inappropriate

This paper was beautifully written. I did have a few objections to how well he developed the underlying principles in accounting for his model.

report post as inappropriate

report post as inappropriate

Dear Armin,

So many essays but once yours came up I made it a point to see what's on offer. Generally, I was not disappointed. A great contribution. As your math is more advanced than mine, I will restrict my questions/ comments to other aspects:

- Your “actual” and “actualizable” are a continuation from your previous ideas. I can't recall if we agreed then that these can be representable as binary digits 1 and 0. Is there an agreement?

- You note that mathematics is not equipped to transcribe phrases like “the absence of” and also say, "everything represented by mathematics is represented as an actuality". And I wish to ask, can something represented by mathematics perish or is it eternally existing? This may be related to the difficulty math has with "the absence of" as you mentioned.

In my essay, I attribute this ultimately to a Parmenidean spell cast on our physics and mathematics, which must be exorcised. Here your superior math skills may be able to view the ideas and put in mathematical language.

Regards,

Akinbo

*I still recall your 'photon existence paradox' for the photon and regret that you recanted on it. It was a paradox that SR would have found almost insurmountable.

report post as inappropriate

So many essays but once yours came up I made it a point to see what's on offer. Generally, I was not disappointed. A great contribution. As your math is more advanced than mine, I will restrict my questions/ comments to other aspects:

- Your “actual” and “actualizable” are a continuation from your previous ideas. I can't recall if we agreed then that these can be representable as binary digits 1 and 0. Is there an agreement?

- You note that mathematics is not equipped to transcribe phrases like “the absence of” and also say, "everything represented by mathematics is represented as an actuality". And I wish to ask, can something represented by mathematics perish or is it eternally existing? This may be related to the difficulty math has with "the absence of" as you mentioned.

In my essay, I attribute this ultimately to a Parmenidean spell cast on our physics and mathematics, which must be exorcised. Here your superior math skills may be able to view the ideas and put in mathematical language.

Regards,

Akinbo

*I still recall your 'photon existence paradox' for the photon and regret that you recanted on it. It was a paradox that SR would have found almost insurmountable.

report post as inappropriate

Dear Akinbo,

Thank you for your feedback. Regarding your comments:

"Your “actual” and “actualizable” are a continuation from your previous ideas. I can't recall if we agreed then that these can be representable as binary digits 1 and 0. Is there an agreement?"

No, I don't think that the distinction can be put in a 1 to 1 correspondence with the digits 0 and 1. If 1...

view entire post

Thank you for your feedback. Regarding your comments:

"Your “actual” and “actualizable” are a continuation from your previous ideas. I can't recall if we agreed then that these can be representable as binary digits 1 and 0. Is there an agreement?"

No, I don't think that the distinction can be put in a 1 to 1 correspondence with the digits 0 and 1. If 1...

view entire post

Dear Armin,

I hopped over and had a quick look at your vixra paper, Do Photons Exist in Spacetime? Although it falls outside the theme of this year's essay contest we can discuss it later.

What I see in the paper is an attempt by you to justify SR by all means by modifying some of the current illogicalities associated with it, one very powerful one unearthed to your credit being that (rearranging your words) "insofar as spacetime is claimed to be the repository of everything that exists, photons do not exist in spacetime". The corrolary to this is that, if photons exist, spacetime is not the repository of everything that exists.

In the early paragraphs you traced the origin of the dilemma. When you have time to spare, read my thoughts HERE and you will understand why your photon existence paradox will be a nightmare for many relativitists.

Your answer regarding the concept of perishing applicable to numbers are enlightening and deserve some more thought by me. Thanks.

Regards,

Akinbo

report post as inappropriate

I hopped over and had a quick look at your vixra paper, Do Photons Exist in Spacetime? Although it falls outside the theme of this year's essay contest we can discuss it later.

What I see in the paper is an attempt by you to justify SR by all means by modifying some of the current illogicalities associated with it, one very powerful one unearthed to your credit being that (rearranging your words) "insofar as spacetime is claimed to be the repository of everything that exists, photons do not exist in spacetime". The corrolary to this is that, if photons exist, spacetime is not the repository of everything that exists.

In the early paragraphs you traced the origin of the dilemma. When you have time to spare, read my thoughts HERE and you will understand why your photon existence paradox will be a nightmare for many relativitists.

Your answer regarding the concept of perishing applicable to numbers are enlightening and deserve some more thought by me. Thanks.

Regards,

Akinbo

report post as inappropriate

Dear Akinbo,

I find it amusing that you interpret my results as a defense of "illogicalities" of special relativity, while I interpret them as support of a unifying idea between quantum theory and SR. Of course, they have already been combined in quantum field theory, but not in a manner in which they can be said to be "unified".

In this contest entry, I presented some theoretical...

view entire post

I find it amusing that you interpret my results as a defense of "illogicalities" of special relativity, while I interpret them as support of a unifying idea between quantum theory and SR. Of course, they have already been combined in quantum field theory, but not in a manner in which they can be said to be "unified".

In this contest entry, I presented some theoretical...

view entire post

Dear Armin Nikkhah Shirazi,

Your essay is very well thought out and enjoyable to read.

Your comment "The freedom to choose any consistent set of axioms entails the freedom to choose exactly those sets which lead to the most effective mathematical representations of a given consistent system, and the requirement of consistency guarantees that how propositions are derived in those models mirrors relationships in the system itself." is very well worded

Your ideas have been supported by ideas from a long time ago "When one accepts one theory and rejects another which is equally consistent with the phenomenon in question, it is clear that one has thereby blundered out of any sort of proper physics and fallen into mythology" – Epicurus, Letter to Pythocles

I agree with the importance of "usefulness" in the evaluation of any set of axioms that help a person may physics predictions. My approach to "usefulness" is a little different then yours, I use visual animations of fundamental particles of the standard model to assist in the understanding of fundamental particles in my essay here. Hope you get a chance offer a rating.

Enjoyable essay to read and best of luck.

Regards,

Ed Unverricht

report post as inappropriate

Your essay is very well thought out and enjoyable to read.

Your comment "The freedom to choose any consistent set of axioms entails the freedom to choose exactly those sets which lead to the most effective mathematical representations of a given consistent system, and the requirement of consistency guarantees that how propositions are derived in those models mirrors relationships in the system itself." is very well worded

Your ideas have been supported by ideas from a long time ago "When one accepts one theory and rejects another which is equally consistent with the phenomenon in question, it is clear that one has thereby blundered out of any sort of proper physics and fallen into mythology" – Epicurus, Letter to Pythocles

I agree with the importance of "usefulness" in the evaluation of any set of axioms that help a person may physics predictions. My approach to "usefulness" is a little different then yours, I use visual animations of fundamental particles of the standard model to assist in the understanding of fundamental particles in my essay here. Hope you get a chance offer a rating.

Enjoyable essay to read and best of luck.

Regards,

Ed Unverricht

report post as inappropriate

Dear Armin,

I agree with you that Feynman was wrong to say no one should understand QM, and then he told physicists wrongly to shut up and just calculate like a dump computer. He might not understand it from his old paradigm perspective but new paradigm like yours and mine KQID would find QM is natural and consistent. For example, it is natural now kids are living in the cyberspace. I agree with you that "all possible outcomes exist merely as potentialities". However, I would argue that since Existence is infinite, it cannot be constrained by finite theory and its finite formulae. The consistent outcomes may also be generated from inconsistent causes.

This essay I think is your best and I vote it accordingly,

Leo KoGuan

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I agree with you that Feynman was wrong to say no one should understand QM, and then he told physicists wrongly to shut up and just calculate like a dump computer. He might not understand it from his old paradigm perspective but new paradigm like yours and mine KQID would find QM is natural and consistent. For example, it is natural now kids are living in the cyberspace. I agree with you that "all possible outcomes exist merely as potentialities". However, I would argue that since Existence is infinite, it cannot be constrained by finite theory and its finite formulae. The consistent outcomes may also be generated from inconsistent causes.

This essay I think is your best and I vote it accordingly,

Leo KoGuan

report post as inappropriate

Dear Leo,

Thank you very much for your feedback. Regarding Feynman, he did not say that no one "should" understand quantum mechanics, but rather that no one does. See the short clip below to see how he meant it:

https://www.youtube.com/watch?v=w3ZRLllWgHI

Also, "shut up and calculate" is widely attributed to Feynman but was actually said by N. David Mermin, see his article here:

http://www.gnm.cl/emenendez/uploads/Cursos/callate-y-ca

lcula.pdf

As far as new paradigms are concerned, I still have a lot of work to do, but I hope that this is a solid step in that direction.

I will read your paper and give feedback shortly, thank you again,

Armin

Thank you very much for your feedback. Regarding Feynman, he did not say that no one "should" understand quantum mechanics, but rather that no one does. See the short clip below to see how he meant it:

https://www.youtube.com/watch?v=w3ZRLllWgHI

Also, "shut up and calculate" is widely attributed to Feynman but was actually said by N. David Mermin, see his article here:

http://www.gnm.cl/emenendez/uploads/Cursos/callate-y-ca

lcula.pdf

As far as new paradigms are concerned, I still have a lot of work to do, but I hope that this is a solid step in that direction.

I will read your paper and give feedback shortly, thank you again,

Armin

Dear Armin,

While you explore the Unreasonable Effectiveness of Mathematics, with Quantum Mechanics; I think your conclusion on the Mysterious Connection between Physics and Mathematics seems to be a trick, as the axioms ascribed for the required consistency with Quantum Mechanics is imaginary.

Whereas this Mysterious Connection is a truth while we explore the Universe with Continuum Mechanics.

With best wishes,

Jayakar

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While you explore the Unreasonable Effectiveness of Mathematics, with Quantum Mechanics; I think your conclusion on the Mysterious Connection between Physics and Mathematics seems to be a trick, as the axioms ascribed for the required consistency with Quantum Mechanics is imaginary.

Whereas this Mysterious Connection is a truth while we explore the Universe with Continuum Mechanics.

With best wishes,

Jayakar

report post as inappropriate

Dear Gordon,

Thank you for your comments. I understand that you consider yourself a local realist. Then how can you at the same time assent to Bohr's statement that "the result of a 'measurement’ does not in general reveal some preexisting property of the ‘system’, but is a product of both ‘system’ and ‘apparatus’,"?

It seems to me that the hallmark of realism is the assumption that generally the system has pre-existing properties. I think if you can explain to me how you reconcile the two, then this will go a long way towards me being able to understand your point of view.

Armin

Thank you for your comments. I understand that you consider yourself a local realist. Then how can you at the same time assent to Bohr's statement that "the result of a 'measurement’ does not in general reveal some preexisting property of the ‘system’, but is a product of both ‘system’ and ‘apparatus’,"?

It seems to me that the hallmark of realism is the assumption that generally the system has pre-existing properties. I think if you can explain to me how you reconcile the two, then this will go a long way towards me being able to understand your point of view.

Armin

Dear Armin,

Thanks for starting at this point, especially as some "local realists" tend avoid it.

I trust we agree that all Nature's extant objects have actual and potential properties?

We then note: Bohr says, "the result of a 'measurement' (with scare quotes) does not in general reveal some pre-existing property." Thus, if I send you a randomly polarised particle, its interaction (without scare quotes) with your polarising apparatus will produce (P>0) a new orientation of polarisation; which is NOT the same as revealing a pre-existing one. Rather

ACTUAL + POTENTIAL -> INTERACTION -> NEW ACTUAL + NEW POTENTIAL.

This is my reason for linking Bohr's view here (not elsewhere) to your own.

BUT now we must clean up these intuitive ideas MATHEMATICALLY.

So, taking care with Nature, we hold a consequence of realism to be: ‘At all times, the set of actual properties possessed by a system (here, particle plus apparatus)* fully determines all relevant probabilities of potential properties of the system.’ See paragraph #2.1, etc., in my essay.

* Including my sister's cat in the system if it might be relevant!

Armin, in closing, and subject to some refinements, I trust we are close to agreement here? More questions, please, if we are not.

With best regards; Gordon Watson: Essay Forum. Essay Only.

report post as inappropriate

Thanks for starting at this point, especially as some "local realists" tend avoid it.

I trust we agree that all Nature's extant objects have actual and potential properties?

We then note: Bohr says, "the result of a 'measurement' (with scare quotes) does not in general reveal some pre-existing property." Thus, if I send you a randomly polarised particle, its interaction (without scare quotes) with your polarising apparatus will produce (P>0) a new orientation of polarisation; which is NOT the same as revealing a pre-existing one. Rather

ACTUAL + POTENTIAL -> INTERACTION -> NEW ACTUAL + NEW POTENTIAL.

This is my reason for linking Bohr's view here (not elsewhere) to your own.

BUT now we must clean up these intuitive ideas MATHEMATICALLY.

So, taking care with Nature, we hold a consequence of realism to be: ‘At all times, the set of actual properties possessed by a system (here, particle plus apparatus)* fully determines all relevant probabilities of potential properties of the system.’ See paragraph #2.1, etc., in my essay.

* Including my sister's cat in the system if it might be relevant!

Armin, in closing, and subject to some refinements, I trust we are close to agreement here? More questions, please, if we are not.

With best regards; Gordon Watson: Essay Forum. Essay Only.

report post as inappropriate

Dear Gordon,

Thank you for your explanation. I think you have misinterpreted Bohr's statement. At any rate, that doesn't matter, because what is relevant is whether your view and mine agree, and unfortunately, it seems that there are some major differences. It already begins with your statement: "if I send you a randomly polarised particle..."

I thought from my essay it would have been obvious that I am pursuing the interpretation according to which there is no particle before the measurement event. And if there is no particle, there is no particle property (which I believe is what Bohr's statement amounts to). There is nothing that is polarised, whether randomly or not.

From my point of view, the particle "comes into existence" as an actual spacetime object upon the interaction with the apparatus we call a "measurement", and the state of the actual spacetime system during the measurement (particle plus apparatus) is determined by the relative contribution of all the actualizabilities associated with the underlying object described by the incomplete spacetime vector, and these contributions map the actualizabilities to the concept of a probability amplitude.

So, to see whether our views agree, you need to just answer this question: In these correlation experiments, are there according to your theory particles between measurements or not? My impression is that there are, and this would be consistent with the fact that you call your theory "realist". However, it would be inconsistent with what I am working on.

Best wishes,

Armin

Thank you for your explanation. I think you have misinterpreted Bohr's statement. At any rate, that doesn't matter, because what is relevant is whether your view and mine agree, and unfortunately, it seems that there are some major differences. It already begins with your statement: "if I send you a randomly polarised particle..."

I thought from my essay it would have been obvious that I am pursuing the interpretation according to which there is no particle before the measurement event. And if there is no particle, there is no particle property (which I believe is what Bohr's statement amounts to). There is nothing that is polarised, whether randomly or not.

From my point of view, the particle "comes into existence" as an actual spacetime object upon the interaction with the apparatus we call a "measurement", and the state of the actual spacetime system during the measurement (particle plus apparatus) is determined by the relative contribution of all the actualizabilities associated with the underlying object described by the incomplete spacetime vector, and these contributions map the actualizabilities to the concept of a probability amplitude.

So, to see whether our views agree, you need to just answer this question: In these correlation experiments, are there according to your theory particles between measurements or not? My impression is that there are, and this would be consistent with the fact that you call your theory "realist". However, it would be inconsistent with what I am working on.

Best wishes,

Armin

This is getting curiouser and curiouser.

*"I thought from my essay it would have been obvious that I am pursuing the interpretation according to which there is no particle before the measurement event"*

Sounds like, the Moon is not there when nobody is looking.

Regards,

Akinbo

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Sounds like, the Moon is not there when nobody is looking.

Regards,

Akinbo

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Thank you for reading my essay: mine is not courage, it is absolute disinterest in the voting mechanism, that permit me to completely freeing the imagination, and narrative.

It is interesting your essay, but I am not convinced that there is not inconsistence in some physical results.

It should create a physical system that reflect on itself, a system with a feedback to measure itself, to create contradiction: each measure of a system, that it is denied by the apparatus, and that it is used to measure the state; I am thinking two Schrodinger's cats, where the measure of the quantum death of the cat destroy the hydrocyanic poison of the other cat, and the life of the cat activate the hydrocyanic poison of the other cat, I think that there is contradiction in the quantum description (some simpler system could be created).

The modal logic, if I understand the concepts, seem to extend the Peano arithmetic to the real number, where the Godel's incompletess theorem is not valid.

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It is interesting your essay, but I am not convinced that there is not inconsistence in some physical results.

It should create a physical system that reflect on itself, a system with a feedback to measure itself, to create contradiction: each measure of a system, that it is denied by the apparatus, and that it is used to measure the state; I am thinking two Schrodinger's cats, where the measure of the quantum death of the cat destroy the hydrocyanic poison of the other cat, and the life of the cat activate the hydrocyanic poison of the other cat, I think that there is contradiction in the quantum description (some simpler system could be created).

The modal logic, if I understand the concepts, seem to extend the Peano arithmetic to the real number, where the Godel's incompletess theorem is not valid.

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Dear Domenico,

Thank you for reading my essay and for your comments. Yes, disinterest is one of the greatest guarantors of freedom (and power, I might add).

If I am understanding your comment about my essay correctly, you have some skepticism about the consistency of standard quantum mechanics. If this is really the case, then I am very surprised by your nonchalance in giving a possible counter example. Proving quantum mechanics inconsistent would seem to be a an extraordinarily huge deal! Is that some more of that disinterest at work?

Although it might be possible, I am not aware of any mechanism by which modal logic permits one to extend the natural numbers to the reals. I use the modality to capture a distinction that cannot be expressed in the language of ordirnary classical logic.

Thanks again for your comments, and if you have any more thoughts about my essay, feel free to express them to me.

Best wishes,

Armin

Thank you for reading my essay and for your comments. Yes, disinterest is one of the greatest guarantors of freedom (and power, I might add).

If I am understanding your comment about my essay correctly, you have some skepticism about the consistency of standard quantum mechanics. If this is really the case, then I am very surprised by your nonchalance in giving a possible counter example. Proving quantum mechanics inconsistent would seem to be a an extraordinarily huge deal! Is that some more of that disinterest at work?

Although it might be possible, I am not aware of any mechanism by which modal logic permits one to extend the natural numbers to the reals. I use the modality to capture a distinction that cannot be expressed in the language of ordirnary classical logic.

Thanks again for your comments, and if you have any more thoughts about my essay, feel free to express them to me.

Best wishes,

Armin

Hi Armin,

I responded to your “kind and heartwarming” comments regarding my Digital Physics movie essay in the discussion forum on my page. I also had some thoughts on your Copenhagen Interpretation youtube video which I included in my response.

Thanks for reading my essay and your interest in the movie! Your FQXi essay, as opposed to more of your youtube videos, will be the next thing I will be taking a look at and commenting on.

Thanks again,

Jon

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I responded to your “kind and heartwarming” comments regarding my Digital Physics movie essay in the discussion forum on my page. I also had some thoughts on your Copenhagen Interpretation youtube video which I included in my response.

Thanks for reading my essay and your interest in the movie! Your FQXi essay, as opposed to more of your youtube videos, will be the next thing I will be taking a look at and commenting on.

Thanks again,

Jon

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Dear Armin,

I also belief, that the distinction between actuality and possibility is needed to give a consistent interpretation of quantum mechanics. In my essay – following Carl Friedrich von Weizsäcker - the time structure is essential. The past being factual (something has happened or not), the future being possible. Mathematics is then the imagination of possible acts in the future, which would lead to a constructivistic justification of mathematics. What role plays time in your theory?

I’d would be happy you could read my essay and comment on it.

Many thanks

Luca

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I also belief, that the distinction between actuality and possibility is needed to give a consistent interpretation of quantum mechanics. In my essay – following Carl Friedrich von Weizsäcker - the time structure is essential. The past being factual (something has happened or not), the future being possible. Mathematics is then the imagination of possible acts in the future, which would lead to a constructivistic justification of mathematics. What role plays time in your theory?

I’d would be happy you could read my essay and comment on it.

Many thanks

Luca

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Dear Luca,

Thank you for your comments, I will leave some remarks on your site as well.

In answer to your questions, time plays multiple roles in my framework. this manifests itself among other things in the following:

1. There is a semantic duality between actualizability in the present world and actuality in a possible future worlds. For that reason my logical operators could also be regarded as temporal modal operators.

2. The frame work explains quantum phenomena in terms of the absence of a characterization in terms of a (spacetime) coordinate time.

3. The axiom takes us from the absence of this association to a superposition of two time directionalities, thereby connecting it both with the Born Rule and the fact that the differential equation that gives the time-evolution of quantum states (i.e. the Schroedinger equation) is time symmetric.

There are other roles for time which I cannot get into actually talking about the physics that this mathematical framework is meant to support, but in short, the concept of time is essential.

Thank you and best wishes,

Armin

Thank you for your comments, I will leave some remarks on your site as well.

In answer to your questions, time plays multiple roles in my framework. this manifests itself among other things in the following:

1. There is a semantic duality between actualizability in the present world and actuality in a possible future worlds. For that reason my logical operators could also be regarded as temporal modal operators.

2. The frame work explains quantum phenomena in terms of the absence of a characterization in terms of a (spacetime) coordinate time.

3. The axiom takes us from the absence of this association to a superposition of two time directionalities, thereby connecting it both with the Born Rule and the fact that the differential equation that gives the time-evolution of quantum states (i.e. the Schroedinger equation) is time symmetric.

There are other roles for time which I cannot get into actually talking about the physics that this mathematical framework is meant to support, but in short, the concept of time is essential.

Thank you and best wishes,

Armin

Hi Armin,

I must admit, learning a new form of logic is difficult, but I still want to ask you some questions even though I did not grasp all of your essay.

Do you think in your model where you consider a quantum 2-D object which has the potential to become a 3-D object (instead of a 3-D object with one dimension consisting of every possible value) you could still account for...

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I must admit, learning a new form of logic is difficult, but I still want to ask you some questions even though I did not grasp all of your essay.

Do you think in your model where you consider a quantum 2-D object which has the potential to become a 3-D object (instead of a 3-D object with one dimension consisting of every possible value) you could still account for...

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Dear Jon,

Thank you for your comments and for your questions. I will try to answer them as best as I can. Keep in mind that I have not yet completely worked out everything, but I like to think that I am close.

"Do you think in your model where you consider a quantum 2-D object which has the potential to become a 3-D object (instead of a 3-D object with one dimension consisting of...

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Thank you for your comments and for your questions. I will try to answer them as best as I can. Keep in mind that I have not yet completely worked out everything, but I like to think that I am close.

"Do you think in your model where you consider a quantum 2-D object which has the potential to become a 3-D object (instead of a 3-D object with one dimension consisting of...

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Thanks for such a detailed response! Still thinking about stuff... More to come soon...

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Dear Armin,

You commented upon my paper so early in the process that I've been under the impression that I had read your essay and commented on it. I see that is not the case. As you've recently returned to offer valuable suggestions, I thank you for those and offer my views on your essay.

You begin by extolling the freedom to choose one's starting assumptions as a great virtue of...

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You commented upon my paper so early in the process that I've been under the impression that I had read your essay and commented on it. I see that is not the case. As you've recently returned to offer valuable suggestions, I thank you for those and offer my views on your essay.

You begin by extolling the freedom to choose one's starting assumptions as a great virtue of...

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Dear Edwin,

Thank you for your comments, let me just give a few clarifications on your summary of my ideas.

1. My framework is based on a combination of free logic and modal logic, however, I am looking into ways of simplifying it so that possibly only one kind of extension of classical logic is needed.

2. Your comparison between the states in 2-D Hilbert Space and the "self-licking ice cone" is funny, but I think it understates the fact that it is already capable of modeling classically highly unexpected behaviors, and yes, I am thinking of the sequential SG experiments with B-fields aligned along different axes. I know that you deny that the actual experiment is modeled by it, but this does not take anything away from the fact that, as a model, it makes non-trivial non-classical predictions and serves as an excellent way for understanding higher-dimensional Hilbert Spaces.

3. I think Matt Leifer's claim about the quantum state was not about wondering whether it is a superposition state or not, but about wondering about its ontological status.

4. The theorem that connects my ideas to the path integral was the center-piece of the essay. In my opinion, there are nowadays so many reformulations of quantum mechanics that it has become a veritable cottage industry, and the problem which, as far as I know, most if not all seem to have in common is that they don't make it any clearer what is "really" going on. I like to think that my model does. Although I don't know anything about your automatic physics, if it is based on automata, then the first question I would have is what objects in the real world these automata correspond to. Without this information, it would seem like it is just another "black box" reformulation.

Thank you again for taking the time to write your comments.

Best wishes,

Armin

Thank you for your comments, let me just give a few clarifications on your summary of my ideas.

1. My framework is based on a combination of free logic and modal logic, however, I am looking into ways of simplifying it so that possibly only one kind of extension of classical logic is needed.

2. Your comparison between the states in 2-D Hilbert Space and the "self-licking ice cone" is funny, but I think it understates the fact that it is already capable of modeling classically highly unexpected behaviors, and yes, I am thinking of the sequential SG experiments with B-fields aligned along different axes. I know that you deny that the actual experiment is modeled by it, but this does not take anything away from the fact that, as a model, it makes non-trivial non-classical predictions and serves as an excellent way for understanding higher-dimensional Hilbert Spaces.

3. I think Matt Leifer's claim about the quantum state was not about wondering whether it is a superposition state or not, but about wondering about its ontological status.

4. The theorem that connects my ideas to the path integral was the center-piece of the essay. In my opinion, there are nowadays so many reformulations of quantum mechanics that it has become a veritable cottage industry, and the problem which, as far as I know, most if not all seem to have in common is that they don't make it any clearer what is "really" going on. I like to think that my model does. Although I don't know anything about your automatic physics, if it is based on automata, then the first question I would have is what objects in the real world these automata correspond to. Without this information, it would seem like it is just another "black box" reformulation.

Thank you again for taking the time to write your comments.

Best wishes,

Armin

Hi Armin –

A very interesting and clearly written essay. I recognized your “default specification axiom” from your 2013 FQXi paper, and I agree that a crucial step toward making quantum theory make sense is to learn how to imagine a world in which possibility plays a fundamental role.

I was struck by your statement that “the state of early 21st century mathematics is such...

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A very interesting and clearly written essay. I recognized your “default specification axiom” from your 2013 FQXi paper, and I agree that a crucial step toward making quantum theory make sense is to learn how to imagine a world in which possibility plays a fundamental role.

I was struck by your statement that “the state of early 21st century mathematics is such...

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Dear Conrad,

Thank you very much for your feedback on my essay. Allow me to comment on some of the things you wrote:

"I recognized your “default specification axiom” from your 2013 FQXi paper, and I agree that a crucial step toward making quantum theory make sense is to learn how to imagine a world in which possibility plays a fundamental role."

Yes, but note that when I...

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Thank you very much for your feedback on my essay. Allow me to comment on some of the things you wrote:

"I recognized your “default specification axiom” from your 2013 FQXi paper, and I agree that a crucial step toward making quantum theory make sense is to learn how to imagine a world in which possibility plays a fundamental role."

Yes, but note that when I...

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Armin –

I appreciate your clarification on “modal” mathematics and probability theory. I believe you're exactly right that someday “it will be very difficult to understand how this could have been overlooked for so long...” – though I’m not sure that such situations are so extremely rare, at least in philosophy. It seems to me that at bottom, the whole history of our intellectual tradition is about learning how to pay attention to aspects of existence that we all grow up taking for granted. At any rate, my own work is entirely a struggle to make certain things explicit that we all know very well – for example, that physical things are observable. And there’s nothing we take more for granted than the possibility of things.

I happened to see your 2012 essay a few days ago, and I wondered how I could have missed it when it first appeared. It looks very interesting, and the title itself should have grabbed my attention, since I’ve always been suspicious of “unification” as the key to fundamental physics. And, your Metatheory diagram is a little like one I put up on my wall decades ago, and keep coming back to, despite my feelings of inadequacy in the face of such a task. So I’ll respond at more length once I’ve had a chance to read that essay carefully.

Thanks – Conrad

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I appreciate your clarification on “modal” mathematics and probability theory. I believe you're exactly right that someday “it will be very difficult to understand how this could have been overlooked for so long...” – though I’m not sure that such situations are so extremely rare, at least in philosophy. It seems to me that at bottom, the whole history of our intellectual tradition is about learning how to pay attention to aspects of existence that we all grow up taking for granted. At any rate, my own work is entirely a struggle to make certain things explicit that we all know very well – for example, that physical things are observable. And there’s nothing we take more for granted than the possibility of things.

I happened to see your 2012 essay a few days ago, and I wondered how I could have missed it when it first appeared. It looks very interesting, and the title itself should have grabbed my attention, since I’ve always been suspicious of “unification” as the key to fundamental physics. And, your Metatheory diagram is a little like one I put up on my wall decades ago, and keep coming back to, despite my feelings of inadequacy in the face of such a task. So I’ll respond at more length once I’ve had a chance to read that essay carefully.

Thanks – Conrad

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Dear Mr. Shirazi,

I have no wish to be disrespectful to you or to your essay, but I think abstract mathematics and abstract physics have nothing to do with how the real Universe is occurring for the following real reason:

Do let me know what you think about this: This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein...

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I have no wish to be disrespectful to you or to your essay, but I think abstract mathematics and abstract physics have nothing to do with how the real Universe is occurring for the following real reason:

Do let me know what you think about this: This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein...

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Dear Joe,

First, a quick correction, my last name is Nikkhah Shirazi, but I understand that it is easy to think the first part is my middle name.

Second, thank you for sharing your views.

Best,

Armin

First, a quick correction, my last name is Nikkhah Shirazi, but I understand that it is easy to think the first part is my middle name.

Second, thank you for sharing your views.

Best,

Armin

Dear Armin,

Thank you for not reporting my comment to FQXi.org as being inappropriate and have the Moderator classify it as Obnoxious Spam.

Gratefully,

Joe Fisher

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Thank you for not reporting my comment to FQXi.org as being inappropriate and have the Moderator classify it as Obnoxious Spam.

Gratefully,

Joe Fisher

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Dear Armin,

Still waiting for answer to my little question asked on 'Akinbo Ojo replied on Mar. 17, 2015 @ 11:35 GMT'.

Thanks and best regards,

Akinbo

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Still waiting for answer to my little question asked on 'Akinbo Ojo replied on Mar. 17, 2015 @ 11:35 GMT'.

Thanks and best regards,

Akinbo

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Dear Akinbo,

Thank you for your patience, I had some other issues to take care of before I could continue our debate, and I knew this post was going to be a long one.

I will get to your question towards the end of this post, but I would like to first address the issues surrounding the questions I asked of you.

First, let me at least give a sketch of an intuitive qualitative...

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Thank you for your patience, I had some other issues to take care of before I could continue our debate, and I knew this post was going to be a long one.

I will get to your question towards the end of this post, but I would like to first address the issues surrounding the questions I asked of you.

First, let me at least give a sketch of an intuitive qualitative...

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Dear Armin,

I must first thank you for the great length and effort you have taken to elaborate further on your viewpoint. I cannot dismiss all what you have said with a wave of the hand but if you will pardon my say so, I see a brilliant mind toiling honestly and laboriously on a road to which he was led by the misplaced confidence in and mis-directions from others. I believe you are...

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I must first thank you for the great length and effort you have taken to elaborate further on your viewpoint. I cannot dismiss all what you have said with a wave of the hand but if you will pardon my say so, I see a brilliant mind toiling honestly and laboriously on a road to which he was led by the misplaced confidence in and mis-directions from others. I believe you are...

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Dear Akinbo,

I suppose nothing I say is going to change your perception that I am desperately clinging to SR in the face of puzzles like the existence paradox (and even the other ones I pointed out in my existence of photons paper), which should have dissuaded me from accepting the theory.

But, being the optimist that I am, let me just emphasize one last time that the reason I accept...

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I suppose nothing I say is going to change your perception that I am desperately clinging to SR in the face of puzzles like the existence paradox (and even the other ones I pointed out in my existence of photons paper), which should have dissuaded me from accepting the theory.

But, being the optimist that I am, let me just emphasize one last time that the reason I accept...

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Dear Armin

Congratulations on your new research, even though I must admit I got lost after the word "modal" - as an artist and inventor my thinking is very pragmatic and mechanical. I rejoined you when “conservation of angular momentum” came up because that is of the essence in my Beautiful Universe BU theory wherein - as I have explained in my essay - physics and mathematics become one at this very basic level of nodes echanging angular momentum causally and locally with adjacent nodes, as in an abacus. I also empathized with your words "pseudo-nonlocality" because in BU angular momentum is transmitted node to ether node as in a slippery gear train and nothing is lost or hidden. Did you read Klingman's essay debunking Bell's theorem in this contest? You lost me in your next section about the path integral because you take quantum probability as a given, which I think is only a mathematical analogy.

Time to listen to music- I hope you are still composing!

Best wishes and appreciation

Vladimir

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Congratulations on your new research, even though I must admit I got lost after the word "modal" - as an artist and inventor my thinking is very pragmatic and mechanical. I rejoined you when “conservation of angular momentum” came up because that is of the essence in my Beautiful Universe BU theory wherein - as I have explained in my essay - physics and mathematics become one at this very basic level of nodes echanging angular momentum causally and locally with adjacent nodes, as in an abacus. I also empathized with your words "pseudo-nonlocality" because in BU angular momentum is transmitted node to ether node as in a slippery gear train and nothing is lost or hidden. Did you read Klingman's essay debunking Bell's theorem in this contest? You lost me in your next section about the path integral because you take quantum probability as a given, which I think is only a mathematical analogy.

Time to listen to music- I hope you are still composing!

Best wishes and appreciation

Vladimir

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Dear Vladimir,

Thank you for your comments. It is too bad that you got lost after the word "modal", if anything I would have expected that as an artist you might actually appreciate it because there is a neat analogy to color and painting:

Working within classical logic is like being able to paint only using black and white as available colors. But because the only limit on finding interpretations for modalities is one's imagination, working within modal logic is like painting using many more different colors. The fact that modalities capture subtle nuances in meaning is like having access to a rich palette of colors to paint subtle nuances that you see in your mind's eye.

"I also empathized with your words "pseudo-nonlocality" because in BU angular momentum is transmitted node to ether node as in a slippery gear train and nothing is lost or hidden"

Well, the "pseudo" in pseudo-nonlocality in my theory comes out of something that most opponents of non-locality would probably not find palatable, namely a radical non-realism according to which there is "nothing" (i.e. no spacetime object) in between quantum measurements. This ensures that there are no "beables" in Bell's sense (The absence of a "beable" is what marks the ontological significance of the incomplete spacetime vector), and so there is nothing that could receive a non-local influence. In my view, Bell's arguments for non-locality are in and of themselves correct, but they simply fail to apply because they require "beables" in order to do so.

"Did you read Klingman's essay debunking Bell's theorem in this contest?"

Yes, I read his essay and found that he did no such thing. What he did is to point out the possibility that a particular experiment (the SG experiment) that could be used to test (really, I should say check its applicability to) Bell's theorem might not be appropriately modeled by Bell's theorem. While I doubt that he is correct I don't think it is impossible, but even if he is right then this has nothing to do with the correctness of Bell's theorem, because the theorem stands independently of any experiment.

Bell's theorem is a mathematical theorem, and trying to debunk it is like trying to debunk the theorem that the product of the number 1 and the number -1 is something other than -1. The only way this could be done is by changing some axioms in the foundations of mathematics, but that would have the highly unwelcome side effect that a whole host of other intuitive commonsense results would become mathematically invalid.

Also, I am a bit disturbed by how quickly you were willing to jump on his "debunking" claim, presumably because it agrees with your metaphysical preferences. Let me just mention that the mark of good science is applying one's skepticism to new claims equally and without regard to whether they agree with one's philosophical predilections or not. Few people may achieve perfection in this regard, but it is a goal that should be aspired to.

"You lost me in your next section about the path integral because you take quantum probability as a given, which I think is only a mathematical analogy."

It's too bad that I lost you in section 6 because that is the heart of my paper. It shows directly, by means of a theorem, the connection between the novel objects definable under an expanded foundation for mathematics and quantum mechanics.

Also, it is not the case that I took probability as a given. Rather, I showed (although omitting a lot of details) that the concept of probability is one of the thing that arises from the the application of axiom D, and then applied the example at the end of section 3, which pertains to an incomplete space vector, in section 6 to an incomplete spacetime vector, thereby setting the stage for deriving the Feynman path integral.

"Time to listen to music- I hope you are still composing!"

Well, thank you, yes as a matter of fact I still am. Last year I composed nearly 25 new pieces, so that my total is now up to almost 140. This year, I have not taken the time to compose because I am trying to focus filling in all the details of my theory.

Thank you again for your comments, I will read your essay shortly and leave some comments.

All the best,

Armin

Thank you for your comments. It is too bad that you got lost after the word "modal", if anything I would have expected that as an artist you might actually appreciate it because there is a neat analogy to color and painting:

Working within classical logic is like being able to paint only using black and white as available colors. But because the only limit on finding interpretations for modalities is one's imagination, working within modal logic is like painting using many more different colors. The fact that modalities capture subtle nuances in meaning is like having access to a rich palette of colors to paint subtle nuances that you see in your mind's eye.

"I also empathized with your words "pseudo-nonlocality" because in BU angular momentum is transmitted node to ether node as in a slippery gear train and nothing is lost or hidden"

Well, the "pseudo" in pseudo-nonlocality in my theory comes out of something that most opponents of non-locality would probably not find palatable, namely a radical non-realism according to which there is "nothing" (i.e. no spacetime object) in between quantum measurements. This ensures that there are no "beables" in Bell's sense (The absence of a "beable" is what marks the ontological significance of the incomplete spacetime vector), and so there is nothing that could receive a non-local influence. In my view, Bell's arguments for non-locality are in and of themselves correct, but they simply fail to apply because they require "beables" in order to do so.

"Did you read Klingman's essay debunking Bell's theorem in this contest?"

Yes, I read his essay and found that he did no such thing. What he did is to point out the possibility that a particular experiment (the SG experiment) that could be used to test (really, I should say check its applicability to) Bell's theorem might not be appropriately modeled by Bell's theorem. While I doubt that he is correct I don't think it is impossible, but even if he is right then this has nothing to do with the correctness of Bell's theorem, because the theorem stands independently of any experiment.

Bell's theorem is a mathematical theorem, and trying to debunk it is like trying to debunk the theorem that the product of the number 1 and the number -1 is something other than -1. The only way this could be done is by changing some axioms in the foundations of mathematics, but that would have the highly unwelcome side effect that a whole host of other intuitive commonsense results would become mathematically invalid.

Also, I am a bit disturbed by how quickly you were willing to jump on his "debunking" claim, presumably because it agrees with your metaphysical preferences. Let me just mention that the mark of good science is applying one's skepticism to new claims equally and without regard to whether they agree with one's philosophical predilections or not. Few people may achieve perfection in this regard, but it is a goal that should be aspired to.

"You lost me in your next section about the path integral because you take quantum probability as a given, which I think is only a mathematical analogy."

It's too bad that I lost you in section 6 because that is the heart of my paper. It shows directly, by means of a theorem, the connection between the novel objects definable under an expanded foundation for mathematics and quantum mechanics.

Also, it is not the case that I took probability as a given. Rather, I showed (although omitting a lot of details) that the concept of probability is one of the thing that arises from the the application of axiom D, and then applied the example at the end of section 3, which pertains to an incomplete space vector, in section 6 to an incomplete spacetime vector, thereby setting the stage for deriving the Feynman path integral.

"Time to listen to music- I hope you are still composing!"

Well, thank you, yes as a matter of fact I still am. Last year I composed nearly 25 new pieces, so that my total is now up to almost 140. This year, I have not taken the time to compose because I am trying to focus filling in all the details of my theory.

Thank you again for your comments, I will read your essay shortly and leave some comments.

All the best,

Armin

Dear Sir, This essay started out as interesting but then went in a direction I don't follow. I was entirely puzzled by your failure to define inconsistency. I am more concerned by why physicists claim Einstein relativity is consistent mathematics when people knowing only high school math can see it is inconsistent. It seems anyone with a high school math background can see that relativity is mathematically inconsistent while experts can not recognize this fact at all and insist that the theory is not inconsistent. It obviously is false and wrong but not inconsistent? That is a puzzle, and so I think inconsistency is not a sufficient criterion. I think you guys need to think out the fundamentals better before you construct your theories.

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Dear Harry,

Thank you for your comments. I am a bit surprised about your comments about special relativity because it was barely mentioned in my paper. In fact, the main result, the theorem on page 8 is expressly in the non-relativistic limit. You are correct that I did not define inconsistency; the reason was that I thought it would be reasonable to expect the reader to know this. If the reader doesn't know what an inconsistency is, then there is little hope they will understand the rest of my essay.

"It seems anyone with a high school math background can see that relativity is mathematically inconsistent while experts can not recognize this fact at all and insist that the theory is not inconsistent.

Well, why do you think it seems that way? Could it be because there is a grand conspiracy among physicists, mathematicians and nuclear engineers worldwide to impose on the rest an obviously false theory, presumably fudging all the technological innovations and experiments based on it, like nuclear reactors, atomic bombs, astrophysical observations, particle accelerators, GPS devices, not to mention all the physics labs so that each new generation of physicists gets brainwashed to join the grand conspiracy? Or could it be because if someone with a high school background misunderstands relativity and, in best Dunning-Kruger form, blames the theory and everyone who uses it for his misunderstanding?

I think I have a good idea which one you think is more likely.

Best,

Armin

Thank you for your comments. I am a bit surprised about your comments about special relativity because it was barely mentioned in my paper. In fact, the main result, the theorem on page 8 is expressly in the non-relativistic limit. You are correct that I did not define inconsistency; the reason was that I thought it would be reasonable to expect the reader to know this. If the reader doesn't know what an inconsistency is, then there is little hope they will understand the rest of my essay.

"It seems anyone with a high school math background can see that relativity is mathematically inconsistent while experts can not recognize this fact at all and insist that the theory is not inconsistent.

Well, why do you think it seems that way? Could it be because there is a grand conspiracy among physicists, mathematicians and nuclear engineers worldwide to impose on the rest an obviously false theory, presumably fudging all the technological innovations and experiments based on it, like nuclear reactors, atomic bombs, astrophysical observations, particle accelerators, GPS devices, not to mention all the physics labs so that each new generation of physicists gets brainwashed to join the grand conspiracy? Or could it be because if someone with a high school background misunderstands relativity and, in best Dunning-Kruger form, blames the theory and everyone who uses it for his misunderstanding?

I think I have a good idea which one you think is more likely.

Best,

Armin

Harry,

To form an all encompassing opinion, and to know where any conspiracy could be coming from, especially concerning GPS devices and relativity, please find time to read about Ronald Ray Hatch - "born in Freedom, Oklahoma, now of Wilmington, California, received his Bachelor of Science degree in physics and math in 1962 from Seattle Pacific University. He worked at Johns Hopkins...

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To form an all encompassing opinion, and to know where any conspiracy could be coming from, especially concerning GPS devices and relativity, please find time to read about Ronald Ray Hatch - "born in Freedom, Oklahoma, now of Wilmington, California, received his Bachelor of Science degree in physics and math in 1962 from Seattle Pacific University. He worked at Johns Hopkins...

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Dear Akinbo,

"To form an all encompassing opinion, and to know where any conspiracy could be coming from..."

Are you seriously considering the possibility of such a worldwide conspiracy?!?

All those physicists working on the Manhattan project generations before GPS must have done an outstanding job not only maintaining the secrecy of the conspiracy but of giving terrifying...

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"To form an all encompassing opinion, and to know where any conspiracy could be coming from..."

Are you seriously considering the possibility of such a worldwide conspiracy?!?

All those physicists working on the Manhattan project generations before GPS must have done an outstanding job not only maintaining the secrecy of the conspiracy but of giving terrifying...

view entire post

Armin,

Very solid essay worthy of scientific publication. Two comments on ontology.

1- When proven, the (empirical) expectation value can be replaced by its (ontological) equivalent or existence. The probability of finding a particle in one place according to the equation is the same as saying that the equation describes where the particle is more likely to be or exist.

2- Actuality is created when probability is constrained, squeezed. When the infinity edges of the normal distribution are eliminated by constraint, then the distribution becomes a box with quantized modes of existence. Similarly, when we measure a free parameter on a particle, the constraint of measurement creates a temporary quantization of the values obtained for that parameter.

all the bests,

Marcel,

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Very solid essay worthy of scientific publication. Two comments on ontology.

1- When proven, the (empirical) expectation value can be replaced by its (ontological) equivalent or existence. The probability of finding a particle in one place according to the equation is the same as saying that the equation describes where the particle is more likely to be or exist.

2- Actuality is created when probability is constrained, squeezed. When the infinity edges of the normal distribution are eliminated by constraint, then the distribution becomes a box with quantized modes of existence. Similarly, when we measure a free parameter on a particle, the constraint of measurement creates a temporary quantization of the values obtained for that parameter.

all the bests,

Marcel,

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Dearly Beloved Armin,

Thanks for your all encompassing essay.It is necessarily didactic;a great contribution.

I am especially thrilled over your assertion of mathematics being potentially effective in modelling reality.And even more so with your projection of the human mind as the facilitator of the nexus between physics and mathematics.

Keep on flourishing,

Lloyd Tamarapreye Okoko.

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Thanks for your all encompassing essay.It is necessarily didactic;a great contribution.

I am especially thrilled over your assertion of mathematics being potentially effective in modelling reality.And even more so with your projection of the human mind as the facilitator of the nexus between physics and mathematics.

Keep on flourishing,

Lloyd Tamarapreye Okoko.

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Dear Lloyd,

Thank you for your kind remarks.

Yes, as you can see, most essays here try to explain the relationship between physics and mathematics solely in terms of those fields (and perhaps some philosophy). But it is easy to ignore the fact that we do both activities in our minds, and therefore its role on the connection is less likely to be appreciated. My essay was in part an effort to bring attention to an important factor that might be easily overlooked.

Best wishes,

Armin

Thank you for your kind remarks.

Yes, as you can see, most essays here try to explain the relationship between physics and mathematics solely in terms of those fields (and perhaps some philosophy). But it is easy to ignore the fact that we do both activities in our minds, and therefore its role on the connection is less likely to be appreciated. My essay was in part an effort to bring attention to an important factor that might be easily overlooked.

Best wishes,

Armin

Dear Armin,

Your description of modal logic is perhaps too brief, so a little research was in order before I concluded that modal logic is a solid foundation for your imaginative theory. I am always a bit amazed at the way a versatile mathematical concept can develop from a small number of simple assumptions.

The Peres-Mermin magic square provides an effective analogy, and another interesting subject to research. The grid layout and aim of the game conjure up something like quantum Sudoku.

Anyway, I just wanted to say it is good to see your progress.

Best regards,

Colin

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Your description of modal logic is perhaps too brief, so a little research was in order before I concluded that modal logic is a solid foundation for your imaginative theory. I am always a bit amazed at the way a versatile mathematical concept can develop from a small number of simple assumptions.

The Peres-Mermin magic square provides an effective analogy, and another interesting subject to research. The grid layout and aim of the game conjure up something like quantum Sudoku.

Anyway, I just wanted to say it is good to see your progress.

Best regards,

Colin

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Dear Colin,

Well, thank you for going through the trouble of researching modal logic in order to understand my theory better. I believe that one of the ways in which the mathematics of the future will be different from the mathematics of today is that it will have the power to formally express nuances that today most mathematicians would perhaps not even dream of expressing.

To reiterate a slightly modified analogy to the one I gave in my response to Vladimir Tamari's post, in my view the era of today's mathematics is like the era of black and white movies, and tomorrow's will be, l believe, like that of color films.

As for the subject of contextuality (and pseudo-nonlocality), these are meant merely as intuition building analogies. The hard work of matching the ideas to the known formalism still awaits. I believe the key is for me to understand how the Hilbert space is built up from orthomodular lattices, a subject I plan on learning this summer. Then I can hopefully take the step of showing how the absence of any "beables" in between measurements implies both.

"Anyway, I just wanted to say it is good to see your progress."

Thank you, it is going slower than I hoped, but it is going.

Best wishes,

Armin

Well, thank you for going through the trouble of researching modal logic in order to understand my theory better. I believe that one of the ways in which the mathematics of the future will be different from the mathematics of today is that it will have the power to formally express nuances that today most mathematicians would perhaps not even dream of expressing.

To reiterate a slightly modified analogy to the one I gave in my response to Vladimir Tamari's post, in my view the era of today's mathematics is like the era of black and white movies, and tomorrow's will be, l believe, like that of color films.

As for the subject of contextuality (and pseudo-nonlocality), these are meant merely as intuition building analogies. The hard work of matching the ideas to the known formalism still awaits. I believe the key is for me to understand how the Hilbert space is built up from orthomodular lattices, a subject I plan on learning this summer. Then I can hopefully take the step of showing how the absence of any "beables" in between measurements implies both.

"Anyway, I just wanted to say it is good to see your progress."

Thank you, it is going slower than I hoped, but it is going.

Best wishes,

Armin

Dear Armin,

As I said I would on my essay's forum, I read your essay. I found your introduction very well written: you nicely describe the freedom that we have to choose our mathematical axioms, and the human imagination it takes to "discover" or "stumble upon" effective mathematical models of reality.

Your attempt to formally incorporate in mathematics the distinction between potentiality and actuality is very ambitious. My own view on the subject is that what distinguishes an "actual" (or "physical") mathematical structure from a "regular" (or "potential") one is whether it contains sub-structures that have the correct properties to be "self-aware" and can "feel" the actuality of the mathematical structure "from the inside". Not having enough of a background in your field of research, I have to confess I could not follow your presentation in detail, but it certainly seems interesting! I hope you'll have the chance to continue your research and look forward to what it can teach us about what it means for a mathematical structure to be "actual".

Good luck!

Marc

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As I said I would on my essay's forum, I read your essay. I found your introduction very well written: you nicely describe the freedom that we have to choose our mathematical axioms, and the human imagination it takes to "discover" or "stumble upon" effective mathematical models of reality.

Your attempt to formally incorporate in mathematics the distinction between potentiality and actuality is very ambitious. My own view on the subject is that what distinguishes an "actual" (or "physical") mathematical structure from a "regular" (or "potential") one is whether it contains sub-structures that have the correct properties to be "self-aware" and can "feel" the actuality of the mathematical structure "from the inside". Not having enough of a background in your field of research, I have to confess I could not follow your presentation in detail, but it certainly seems interesting! I hope you'll have the chance to continue your research and look forward to what it can teach us about what it means for a mathematical structure to be "actual".

Good luck!

Marc

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Dear Mark,

Thank you for your comments.

"My own view on the subject is that what distinguishes an "actual" (or "physical") mathematical structure from a "regular" (or "potential") one is whether it contains sub-structures that have the correct properties to be "self-aware" and can "feel" the actuality of the mathematical structure "from the inside"."

I'm afraid I do not quite follow. Can you give an example? Or, how would the thrown coin toss vs. the unthrown one differ according to your view?

"Not having enough of a background in your field of research, I have to confess I could not follow your presentation in detail,"

Well, that's ok because the details have not yet all be worked out, so if you were able to do that, you would have done my work for me;-)

"I hope you'll have the chance to continue your research and look forward to what it can teach us about what it means for a mathematical structure to be "actual"."

Well actually I don't think my work will be able to say anything about what it means for a mathematical structure to be "actual" because, remember from page 2 of my essay, my work is just concerned with mathematics as a representation of objects which in the real world exist as actualities or potentialities.

Thanks again, sorry I did not get any challenges from you:(

Best,

Armin

Thank you for your comments.

"My own view on the subject is that what distinguishes an "actual" (or "physical") mathematical structure from a "regular" (or "potential") one is whether it contains sub-structures that have the correct properties to be "self-aware" and can "feel" the actuality of the mathematical structure "from the inside"."

I'm afraid I do not quite follow. Can you give an example? Or, how would the thrown coin toss vs. the unthrown one differ according to your view?

"Not having enough of a background in your field of research, I have to confess I could not follow your presentation in detail,"

Well, that's ok because the details have not yet all be worked out, so if you were able to do that, you would have done my work for me;-)

"I hope you'll have the chance to continue your research and look forward to what it can teach us about what it means for a mathematical structure to be "actual"."

Well actually I don't think my work will be able to say anything about what it means for a mathematical structure to be "actual" because, remember from page 2 of my essay, my work is just concerned with mathematics as a representation of objects which in the real world exist as actualities or potentialities.

Thanks again, sorry I did not get any challenges from you:(

Best,

Armin

Dear Armin,

You mentioned in your recent reply on my page that it is very hard to make comments that really change the point of view of your interlocutor, and I agree that it is so. I think it's even harder when your interlocutor has a set of basic assumptions about the fundamental nature of things and their relative importance that is completely different from yours.

For you...

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You mentioned in your recent reply on my page that it is very hard to make comments that really change the point of view of your interlocutor, and I agree that it is so. I think it's even harder when your interlocutor has a set of basic assumptions about the fundamental nature of things and their relative importance that is completely different from yours.

For you...

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Hi Marc,

I had been thinking about what might have led you to believe that I would consider abstract mathematical objects as potentialities, and it occurred to me that possibly it was something I said in the conclusion of my essay, namely "...the freedom to choose one’s axioms

coupled with the requirement of consistency should naturally lead us to expect mathematics to be unreasonably effective in modeling reality, but that this unreasonable effectiveness only exists, as it were, as an actualizability..."

If this passage is responsible for that, I'd like to mention that I did not literally mean that undiscovered mathematics exists as an actualizability (as signaled by the words "as it were"). I just phrased it that way because it seemed pleasing to me that the central distinction in the case study was analogical to my overall argument.

Hope this cleared things up a little,

Best wishes,

Armin

PS. When you said that you could not follow my arguments in detail, I missed a chance to ask where you got lost, so that in future expositions I can take greater care to try to explain those parts better. I would still appreciate any constructive criticism in that respect.

I had been thinking about what might have led you to believe that I would consider abstract mathematical objects as potentialities, and it occurred to me that possibly it was something I said in the conclusion of my essay, namely "...the freedom to choose one’s axioms

coupled with the requirement of consistency should naturally lead us to expect mathematics to be unreasonably effective in modeling reality, but that this unreasonable effectiveness only exists, as it were, as an actualizability..."

If this passage is responsible for that, I'd like to mention that I did not literally mean that undiscovered mathematics exists as an actualizability (as signaled by the words "as it were"). I just phrased it that way because it seemed pleasing to me that the central distinction in the case study was analogical to my overall argument.

Hope this cleared things up a little,

Best wishes,

Armin

PS. When you said that you could not follow my arguments in detail, I missed a chance to ask where you got lost, so that in future expositions I can take greater care to try to explain those parts better. I would still appreciate any constructive criticism in that respect.

Dear Marc,

Thank you for engaging with me even after my relatively heavy criticism.

"For you (correct me if I'm wrong), the "real world" is the observable physical universe and mathematics is a way for us humans to represent it: naturally, you find it is most important to study how mathematics does this, and hopefully improve the definition of mathematics to help it do its...

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Thank you for engaging with me even after my relatively heavy criticism.

"For you (correct me if I'm wrong), the "real world" is the observable physical universe and mathematics is a way for us humans to represent it: naturally, you find it is most important to study how mathematics does this, and hopefully improve the definition of mathematics to help it do its...

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Hi Armin/Marc,

Sorry for interrupting, but I hope I can clarify or reconcile some of your differences. The reason is that I think we the three have some things in common that if we put all three then you get a clearer picture.

Marc, you promised you look at my theory and comment but you seem to have been overwhelmed by comments which is understandable. I have already...

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Sorry for interrupting, but I hope I can clarify or reconcile some of your differences. The reason is that I think we the three have some things in common that if we put all three then you get a clearer picture.

Marc, you promised you look at my theory and comment but you seem to have been overwhelmed by comments which is understandable. I have already...

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Dear Adel,

I just left a comment at your blog with some suggestions on how you might make it easier for me (and possibly others) to follow your arguments. You say that I am trying to do what you have done with your simulations, but unfortunately this is far from obvious to me. So let me ask you the following questions (to which I have concrete answers based on the theory that I am pursuing) to see whether our answers match up:

1) You say that your simulation lead to the Schroedinger equation. Where does the imaginary factor i in that equation come from in your simulations?

2) The best I can tell, what you have built is a probabilistic model in which the states should be identified with probabilities, not probability amplitudes. If the states are in fact probability amplitudes, which part of your model leads to that conclusion?

3) How does the exponential phase factor associated with each quantum state arise in your simulation?

4) How do you obtain the Born Rule?

5) How do you formalize the distinction between actuality and potentiality? Note, contrary to your assertions above, my conception of actualizability is not the same as randomness. In particular, I talk about a specific kind of actualizability which I call pro-actuality, and it is as far from randomness as possible: As an example, consider a hypothetical coin which no matter how often you flip it, will alway land on heads. Using standard mathematics, I do not know of a way in which an experiment with such a coin in which you flip it can be distinguished from one in which you don't, because in both cases we would say that the probability of an outcome of heads is 1. Pro-actuality (and actualizability in general) is meant to bring in the distinction between cases in which the event has happened from those in which it has not.

Answering these will go some ways to help me better understand your model.

Best wishes,

Armin

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I just left a comment at your blog with some suggestions on how you might make it easier for me (and possibly others) to follow your arguments. You say that I am trying to do what you have done with your simulations, but unfortunately this is far from obvious to me. So let me ask you the following questions (to which I have concrete answers based on the theory that I am pursuing) to see whether our answers match up:

1) You say that your simulation lead to the Schroedinger equation. Where does the imaginary factor i in that equation come from in your simulations?

2) The best I can tell, what you have built is a probabilistic model in which the states should be identified with probabilities, not probability amplitudes. If the states are in fact probability amplitudes, which part of your model leads to that conclusion?

3) How does the exponential phase factor associated with each quantum state arise in your simulation?

4) How do you obtain the Born Rule?

5) How do you formalize the distinction between actuality and potentiality? Note, contrary to your assertions above, my conception of actualizability is not the same as randomness. In particular, I talk about a specific kind of actualizability which I call pro-actuality, and it is as far from randomness as possible: As an example, consider a hypothetical coin which no matter how often you flip it, will alway land on heads. Using standard mathematics, I do not know of a way in which an experiment with such a coin in which you flip it can be distinguished from one in which you don't, because in both cases we would say that the probability of an outcome of heads is 1. Pro-actuality (and actualizability in general) is meant to bring in the distinction between cases in which the event has happened from those in which it has not.

Answering these will go some ways to help me better understand your model.

Best wishes,

Armin

Dear Armin,

Thank you for your elaborate replies, you have always been my best customer, actually the only real customer. This is exactly what I was hoping to get out of this contest. All your points in your reply in my thread are well taken, but I also have my reasons, I will explain there.

Let me first be clear about an issue which has been raised by you and others. ...

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Thank you for your elaborate replies, you have always been my best customer, actually the only real customer. This is exactly what I was hoping to get out of this contest. All your points in your reply in my thread are well taken, but I also have my reasons, I will explain there.

Let me first be clear about an issue which has been raised by you and others. ...

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Dear Adel,

Just a quick remark that your comment seems to confirm my suspicion that the probabilistic model at which you have arrived is mathematically inequivalent to QM. In and of itself, this is not necessarily a bad thing, if you can squeeze out testable predictions of experiments which have not been performed yet.

But if your goal is to re-derive QM from your model, it really has to be mathematically equivalent. That means that the central differential equation has to be one that is mathematically the same as the Schrodinger equation, including the imaginary factor i.

I understand that your concern is with getting to a more general framework that encompasses QFT, but if you don't pay attention to these intermediate steps, your chances of success will be greatly diminished.

Best,

Armin

Just a quick remark that your comment seems to confirm my suspicion that the probabilistic model at which you have arrived is mathematically inequivalent to QM. In and of itself, this is not necessarily a bad thing, if you can squeeze out testable predictions of experiments which have not been performed yet.

But if your goal is to re-derive QM from your model, it really has to be mathematically equivalent. That means that the central differential equation has to be one that is mathematically the same as the Schrodinger equation, including the imaginary factor i.

I understand that your concern is with getting to a more general framework that encompasses QFT, but if you don't pay attention to these intermediate steps, your chances of success will be greatly diminished.

Best,

Armin

Dear Armin,

You are following a similar route than me about the role of mathematical imagination in giving sense (possibly an interpretation) to strange quantum mechanical facts, such as contextuality. Mermin's square is one of my favorite basic objects on that topic. Usually, one uses counterfactual arguments to justify the paradox and one arrives at the Kochen-Specker theorem (as in Peres'book). You are proposing modal logic and find a kind of incompleteness of the standard description. It is fine. I have not entered the details of your arguments that you recognize preliminary.

I follow you in your aim to invent clever mathematics to clarify the topic. I found another way for contextuality that is based on (Grothendieck's) coset structure of free groups on two generators. Some details are in my essay and in its ref. [17] to appear in Quantum Information Processing. As your essay is interesting, well in the topic, perfectly argued and fits the philosophy I agree with, I am giving it a well deserved high mark.

Best,

Michel

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You are following a similar route than me about the role of mathematical imagination in giving sense (possibly an interpretation) to strange quantum mechanical facts, such as contextuality. Mermin's square is one of my favorite basic objects on that topic. Usually, one uses counterfactual arguments to justify the paradox and one arrives at the Kochen-Specker theorem (as in Peres'book). You are proposing modal logic and find a kind of incompleteness of the standard description. It is fine. I have not entered the details of your arguments that you recognize preliminary.

I follow you in your aim to invent clever mathematics to clarify the topic. I found another way for contextuality that is based on (Grothendieck's) coset structure of free groups on two generators. Some details are in my essay and in its ref. [17] to appear in Quantum Information Processing. As your essay is interesting, well in the topic, perfectly argued and fits the philosophy I agree with, I am giving it a well deserved high mark.

Best,

Michel

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Dear Michel,

Thank you for your comments. Yes, I still need to fill in many more details, which I hope will be forthcoming soon, but it is true that in my view all the "weirdness" associated with QM comes out the fact that the quantum states are spacetime manifestations of objects which are in the sense outlined in my paper incomplete.

I will shortly read your essay as well.

Thank you and best wishes,

Armin

Thank you for your comments. Yes, I still need to fill in many more details, which I hope will be forthcoming soon, but it is true that in my view all the "weirdness" associated with QM comes out the fact that the quantum states are spacetime manifestations of objects which are in the sense outlined in my paper incomplete.

I will shortly read your essay as well.

Thank you and best wishes,

Armin

Dear Michel,

Given that your essay had a strong emphasis on phenomena related to contextuality and non-locality, I thought it would be a good idea to try to clarify one aspect of my paper that you might have come across which I already know others seem to have misunderstood, and which you might have perhaps also found not easy to understand when you read my paper.

I claimed that one...

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Given that your essay had a strong emphasis on phenomena related to contextuality and non-locality, I thought it would be a good idea to try to clarify one aspect of my paper that you might have come across which I already know others seem to have misunderstood, and which you might have perhaps also found not easy to understand when you read my paper.

I claimed that one...

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Dear Armin,

Thanks for the clarifications. Yes, contextuality is a fact of quantum theory confirmed in experiments and it is good that your local "non-realist" approach goes in that direction. I am eager to follow its developement.

Best,

Michel

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Thanks for the clarifications. Yes, contextuality is a fact of quantum theory confirmed in experiments and it is good that your local "non-realist" approach goes in that direction. I am eager to follow its developement.

Best,

Michel

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Hi Armin,

Many thanks for your reply in my forum and specifically for your link to Charles Raldo Cards essay. I think it was a great essay. I also had the chance to read your essay from the It from Bit contest, which I found enlightening. I did not find the time to write a proper reply in my forum, since I found that your description of quantum structures as background dependent has a connection to my try to describe the unitary evolution of a closed system as special case of the system interacting with its interaction field.

However now I can see, that the present work is a continuation of your previous work and it is a create achievement to be able to formalize the Default Specification Principle.

Best regards

Luca

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Many thanks for your reply in my forum and specifically for your link to Charles Raldo Cards essay. I think it was a great essay. I also had the chance to read your essay from the It from Bit contest, which I found enlightening. I did not find the time to write a proper reply in my forum, since I found that your description of quantum structures as background dependent has a connection to my try to describe the unitary evolution of a closed system as special case of the system interacting with its interaction field.

However now I can see, that the present work is a continuation of your previous work and it is a create achievement to be able to formalize the Default Specification Principle.

Best regards

Luca

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Dear Luca,

Thank you for your comments, it is always gratifying to see when others recognize the greater context of the project one is pursuing. In fact, I would say all my previous FQXi essays with the exception of last year's (which was my one and only foray into more political matters) have explored different aspects of the grand scheme, but I do not expect this to be obvious until most of the pieces of the puzzle are in place.

I am glad that you found my essay It, Bit, Object, Background useful. Yes, in my mind, the question about the essence of quantum states and their possible conception as information is inseparable from the question of the relationship of quantum states to a background. Although it is only implicit, the connection is there even in the current work. The path integrals associated with harmonic oscillator and other quantum states with potential states are still more fundamentally describable as in section 6 in terms of an incomplete spacetime vector, so in that sense all quantum states are the same. What gives rise to the different manifestations is the difference in the spacetime background (together with the difference in the phase factor), and I have the impression that you have understood this point.

Best wishes,

Armin

Thank you for your comments, it is always gratifying to see when others recognize the greater context of the project one is pursuing. In fact, I would say all my previous FQXi essays with the exception of last year's (which was my one and only foray into more political matters) have explored different aspects of the grand scheme, but I do not expect this to be obvious until most of the pieces of the puzzle are in place.

I am glad that you found my essay It, Bit, Object, Background useful. Yes, in my mind, the question about the essence of quantum states and their possible conception as information is inseparable from the question of the relationship of quantum states to a background. Although it is only implicit, the connection is there even in the current work. The path integrals associated with harmonic oscillator and other quantum states with potential states are still more fundamentally describable as in section 6 in terms of an incomplete spacetime vector, so in that sense all quantum states are the same. What gives rise to the different manifestations is the difference in the spacetime background (together with the difference in the phase factor), and I have the impression that you have understood this point.

Best wishes,

Armin

Dear Armin,

Great essay! It is well-argued and beautifully written, and it deserves high rating. After reading it, I find that indeed I have a "new appreciation for the role of imagination in mathematics". Good luck in the contest.

All the best,

Mohammed

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Great essay! It is well-argued and beautifully written, and it deserves high rating. After reading it, I find that indeed I have a "new appreciation for the role of imagination in mathematics". Good luck in the contest.

All the best,

Mohammed

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Dear Mohammed,

Thank you for the kind words. Yes, I like to think that though people do mention the role of imagination in mathematics occasionally, they do not really appreciate how crucial it has been to all the advances in the field.

I will shortly leave a comment on your essay and wish you good luck in the contest as well.

Nest,

Armin

Thank you for the kind words. Yes, I like to think that though people do mention the role of imagination in mathematics occasionally, they do not really appreciate how crucial it has been to all the advances in the field.

I will shortly leave a comment on your essay and wish you good luck in the contest as well.

Nest,

Armin

Dear Armin,

thanks for reading my essay and for the comment.

You are right with your objection. My argument was to shortly presented. I had the idea to present a contradiction: math and creativity. Most people see math asa fully rational theory. But you are right also other areas share this property. Maybe one should add: math used creativity and intuition and also pure logic to realize these ideas. But I have to think about it more carefully.

I also read your thoughtful essay and rate them high (9 points). Great example to present the path integral.

Good luck for the contest

Torsten

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thanks for reading my essay and for the comment.

You are right with your objection. My argument was to shortly presented. I had the idea to present a contradiction: math and creativity. Most people see math asa fully rational theory. But you are right also other areas share this property. Maybe one should add: math used creativity and intuition and also pure logic to realize these ideas. But I have to think about it more carefully.

I also read your thoughtful essay and rate them high (9 points). Great example to present the path integral.

Good luck for the contest

Torsten

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Hi Armin--

I have been remiss in not commenting on your essay. I apologize for that and now attempt to make amends.

Your essay is exactly what I would hope for in this contest. It was very thought-provoking and "pushed the envelope". I found much of it to be difficult going, particularly the beginning when you are using logical operator notation (with which I am not overly familiar). Your analysis of QM was much easier going for me and I really admired your style of presentation. Your take on non-locality (pseudo non-locality, to be precise) was well-written and certainly grabbed my attention. Overall, I would have to think much harder on your position before I could sign onto it. However, you got me to thinking--and I see that as the main goal for papers like these.

Quick question: I see certain parallels between your paper and the work of Chiribella, D'Ariano & Perinotti (see, e.g., arXiv:1209:5533v2). Your use of "imagination" and their use of "information" seem to trend in similar directions. Have I got that right? Or have I (inadvertently) mischaracterized your position?

Once again, great job. For what it is worth, I gave you a high rating.

Best regards and best of luck in the contest,

Bill.

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I have been remiss in not commenting on your essay. I apologize for that and now attempt to make amends.

Your essay is exactly what I would hope for in this contest. It was very thought-provoking and "pushed the envelope". I found much of it to be difficult going, particularly the beginning when you are using logical operator notation (with which I am not overly familiar). Your analysis of QM was much easier going for me and I really admired your style of presentation. Your take on non-locality (pseudo non-locality, to be precise) was well-written and certainly grabbed my attention. Overall, I would have to think much harder on your position before I could sign onto it. However, you got me to thinking--and I see that as the main goal for papers like these.

Quick question: I see certain parallels between your paper and the work of Chiribella, D'Ariano & Perinotti (see, e.g., arXiv:1209:5533v2). Your use of "imagination" and their use of "information" seem to trend in similar directions. Have I got that right? Or have I (inadvertently) mischaracterized your position?

Once again, great job. For what it is worth, I gave you a high rating.

Best regards and best of luck in the contest,

Bill.

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Dear Bill,

Thank you for your comments. I regret that you found the logical foundation part of my essay hard going. I could not omit it, because without it the novel mathematical structures that are characterized by incompleteness would seem like non-sense, and I could not describe it more fully, partly because of the length restrictions and partly because I have not yet worked out all the...

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Thank you for your comments. I regret that you found the logical foundation part of my essay hard going. I could not omit it, because without it the novel mathematical structures that are characterized by incompleteness would seem like non-sense, and I could not describe it more fully, partly because of the length restrictions and partly because I have not yet worked out all the...

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Hi Armin,

Would you mind if I tapped your brain a little? I have a draft of a paper, still related to our previous discussion. I put in a casual remark on the 'photon existence paradox'.

Regards,

Akinbo

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Abstract: Absurdities arising from Einstein's velocity-addition law have been discussed since the theory's formulation. Most of these have been dismissed as being philosophical arguments and supporters of Special relativity theory are of the opinion that if the math is not faulted they are ready to live with the paradoxes. Here, we now demonstrate a mathematical contradiction internal to the theory itself. We show that when applied to light there is no way to mathematically reconcile the Einstein velocity-addition law with the second postulate of the theory which may have a fatal consequence.

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attachments: _Shorter_version__Application_of_the_velocity-addition_law_to_light_itself.pdf

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Would you mind if I tapped your brain a little? I have a draft of a paper, still related to our previous discussion. I put in a casual remark on the 'photon existence paradox'.

Regards,

Akinbo

=====================================

====================================

Abstract: Absurdities arising from Einstein's velocity-addition law have been discussed since the theory's formulation. Most of these have been dismissed as being philosophical arguments and supporters of Special relativity theory are of the opinion that if the math is not faulted they are ready to live with the paradoxes. Here, we now demonstrate a mathematical contradiction internal to the theory itself. We show that when applied to light there is no way to mathematically reconcile the Einstein velocity-addition law with the second postulate of the theory which may have a fatal consequence.

================================================

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attachments: _Shorter_version__Application_of_the_velocity-addition_law_to_light_itself.pdf

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