Популярно о конечной математике и ее интересных применениях в квантовой теории

Mark joined Scientific Reports in November 2017 after an undergraduate degree in physics at the University College Cork, Ireland, and PhD at the Okinawa Institute of Science and Technology, Japan. His interests lie in optical manipulation and structured light.

Т.е., у него есть аж PhD. И с таким “высоким” уровнем он думает, что моя статья по чистой математике (а в журнале есть разделы Mathematical Physics, Quantum Physics и др.). Т. е., опять все как обычно, что вопрос о фундаментальной статье, которая меняет стандартные парадигмы по физике и математике решает тот кто понятия не имеет о фундаментальной физике и математике. В инструкции для авторов пишут, что автор должен предложить кто из Editorial Board может быть handling editor. Я предложил Igor Yurkevich, который работает в Aston University, но ему даже не послали. Когда я ему об этом написал, то он ответил. Ответ очень интересный т. к. показывает мнение физика, который в этих кругах:

I am pretty sure that they even did not bother to send abstract to anyone. Usually such an invitation to handle a submission takes a week or so until someone picks it up. If not, they send another "chasing up" invitation to other Editorial Board members. Quick response means that some technical clerk read and decided not to proceed with formalities. This is now standard procedure in Nature and Science publishing journals. Someone's taste decides everything – era of scarce resources!

Т.е., даже высококвалифицированный физик понимает, что что-то не то в королевстве датском, но от высококвалифицированных физиков мало что зависит.

Еще одна попытка – журнал Mathematics, который, вроде бы, высоко не котируется и часто берет работы авторов, которые не в establishment. В отличие от так наз. престижных журналов, здесь отказ мотивировался рецензиями:

Рецензия 1: The Author of submitted manuscript believes that he presents and proofs fundamental ideas concerning general relations between the quantum theory and foundations of mathematics. He refers to the previously published papers (authored by him) and to results presented there. Some of those articles can be found in the references. Those papers were devoted to the finite mathematics and proposed by the Author «finite quantum theory». Unfortunately, it is difficult to judge positively the submitted manuscript. The Author presents in the first part of the paper some historical and philosophical considerations and remarks. Next, the Author presents proposed by him a statement and mathematical proof and discussion (Section 3), and finally, he goes back to the discussion of rather philosophical nature. Concerning the more mathematical part of the manuscript, it contains the figure and some considerations which have already been published by the Author in Physics of Particles and Nuclei Letters 14:77 (2017) – this article was not mentioned in the list of references. Concerning the latter, one can find there only the references to four books devoted to the philosophy and those concerning the papers which were written by the Author. In my opinion, the manuscript does not fit the topic s of the Mathematics journal. Maybe it will be more suitable for publishing in one of the journals devoted to the philosophy. Moreover, the form of the paper does not meet the standards of the journal. Thus, I can conclude that the article should be rejected.

Рецензия 2: This is another paper of the Author dealing with a kind of modular arithmetic and its purported application in physics. The method is motivated by the verification principle. According to Wikipedia (I am not a philosopher and therefore have to rely on external sources), «Verificationism, also known as the verification principle or the verifiability criterion of meaning, is the philosophical doctrine that only statements that are empirically verifiable (i.e. verifiable through the senses) are cognitively meaningful, or else they are truths of logic (tautologies)». This is in contrast to the Author's definition «A proposition is only cognitively meaningful if it can be definitively and conclusively determined to be either true or false (see e.g. Refs. [1])». – the term empirical is missing. Then the Author continues «Popper proposed the concept of falsicationism [3]: If no cases where a claim is false can be found, then the hypothesis is accepted as provisionally true». – I am afraid I am not able to see the relevance of this discussion to the mathematical content. I also find it trivial to demand that «According to the principles of quantum theory, there should be no statements accepted without proof and based on belief in their correctness (i.e. axioms)». This is a rather general principle for physical theories; not only quantum mechanics. I am afraid that the main statement of the paper is almost trivial: «Main Statement: Even classical mathematics itself is a special degenerated case of finite mathematics in the formal limit when the characteristic of the field or ring in the latter goes to infinity». Is that not done in analysis all the time? The Author also misses out the metamathematical debates on *) constructive mathematics; as exposed, e.g., in… и дальше идет список литературы.

Фраза из второй рецензии “Is that not done in analysis all the time?” показывает, что рецензент даже не понимает о чем идет речь. Но первый рецензент, вроде бы, понимает, что проблема фундаментальная. В таком случае, казалось бы, он должен просто сказать, являются ли результаты новыми и правильными. Но он конкретно результаты не рассматривает, а говорит, что статья больше подходит для философского журнала.

Я послал вопрос секретарю журнала Mr Zhang:

Thank you for your email informing about the editorial decision. The referee reports seem to be strange for the following reasons. The referees say that my results are not for a math journal but they do not judge a paper as a math paper. My paper contains new mathematical statements and in my understanding the main goal of the reports is to say whether the proofs are correct and new. However, the reports say nothing specific about this. The referees discuss philosophy, advise me to consider constructive math, finitism etc. but nothing specific is said about my results and one of the referees even says a strange phrase that “Is that not done in analysis all the time?”. As noted in the paper, philosophy is discussed only for illustration while the results are mathematical and do not depend on philosophy.

Let me also note that the special issue is titled «Mathematical Physics II» and I prove that standard quantum theory is a degenerated special case of FQT. This is a fully new result but the referees even do not mention this result. From the reports it is not clear to me whether the referees treat their recommendation as final or they accept that the author has a right to appeal. If I have a chance to appeal, I could try to submit a revised version. Is this acceptable? But to be honest I am puzzled because the reports say nothing specific on whether my results are correct or not. I can include the discussion of constructive math, finitism etc., but the main problem is whether the referees agree that my results are correct and new. Unfortunately, I could not find a clear explanation of this point. I would be grateful for your explanation.

Редактор этого special issue “Mathematical Physics II” – Dr. Enrico De Micheli. Mr Zhang ответил так:

The final decision was made by our academic editor according to his opinion along with the collected reports during the peer review. Hope your gentle understanding. We would like to thank you for having considered Mathematics and wish you every success in the future.

Т.е., редактор принял окончательное решение даже не дав автору права на appeal.

Выше я писал о своей попытке опубликовать статью о проблеме времени в Journal of Physics Communications. После этого решил, что иметь с ними дело бессмысленно. Но получил от них стандартное письмо (которое, наверняка было послано многим) с приглашением послать статью в журнал. Ответил им, что после моего первого опыта не планировал больше посылать им. Но если редакция пришлет мне официальное приглашение на статью https://hal.archives-ouvertes.fr/hal-02262153 в HAL, то эту статью пошлю. И получил такой ответ:

Dear Dr Lev,

Thank you very much for your recent message. We are very sorry to hear about your unfavourable experience with your previous submission to Journal of Physics Communications (JPCO).

With regards to your Article submitted in April-2018, we can see that an Editorial Board member was approached to expedite the review process as a result of difficulty obtaining reviewer reports of a high standard however, none were available to do so. This is a rare occurrence and we apologise for any inconvenience the delayed and ultimately withdrawn article caused. In response to your latter query, we'd be glad to consider your new paper and will strive to obtain quality and efficient reviews to report on the manuscript. Our Editor has viewed the article via the link you provided and advised that it would be a great fit for JPCO. We hope this helps. If there is anything we can assist you with, please don't hesitate to contact us.

Kind regards,

Isabella Formisano & Blythe RowleyEditorial Assistants

Т.е., теперь они дают уже новое объяснение почему отвергли мою статью в апреле 2018 г.: потому что не могли найти рецензента. А дальше они клянутся, что сделают все чтобы получить квалифицированную рецензию на новую статью, что ее смотрел Editor и решил, что она будет a great fit для журнала. Казалось бы, после такого ответа есть надежда, что статья будет рассмотрена по существу. Но после того как послал статью, сразу получил стандартный ответ:

Dear Dr Lev,

Re: "Why Finite Mathematics Is More Fundamental Than Classical One" by Lev, Felix

Article reference: JPCO-101317

Thank you for your submission to Journal of Physics Communications.

To be publishable in this journal, articles must be of high scientific quality and be recognised as making a positive contribution to the literature.

Your Paper has been assessed and has been found not to meet these criteria. It therefore does not warrant publication in Journal of Physics Communications and has been withdrawn from consideration.

We are sorry that we cannot respond more positively and wish you luck in publishing your article elsewhere.

Yours sincerely

Sarah Hunter

Мой ответ на это письмо был такой:

Dear Editors,

After my first experience with JPCO I did not plan to submit new papers. However, in response to Dr. Messaritaki’s invitation I wrote that will submit my paper https://hal.archives-ouvertes.fr/hal-02262153 only if I receive an official invitation to submit this particular paper. In your response of Sep 18th you wrote «In response to your latter query, we'd be glad to consider your new paper and will strive to obtain quality and efficient reviews to report on the manuscript. Our Editor has viewed the article via the link you provided and advised that it would be a great fit for JPCO». However, when I submitted this paper I immediately received a rejection letter. Such an attitude to the author is obviously indecent.

Sincerely, Felix Lev.

Т.е., открытым текстом написал им, что такое отношение к автору неприличное. Вроде бы, после этого они должны обидеться и не иметь дел со мной. Но получил такой ответ:

Dear Dr Lev,

Re: "Why Finite Mathematics Is More Fundamental Than Classical One" by Lev, Felix

Article reference: JPCO-101317

Thank you for your email. We apologise that your paper was rejected. Due to a miscommunication, we were not aware your paper had been commissioned. I have now consulted the Editor and we are happy to reconsider your manuscript and continue processing it in JPCO. Please could you let us know if you are happy for us to continue processing your paper in this journal?

Yours sincerely

Sarah Hunter

Т.е., они извиняются, что произошло miscommunication (т.е., левая рука не знала что делает правая), они пересмотрели свое решение, решили опять рассматривать мою статью и просят сообщить счастлив ли я. Т.е., я послал им статью, написал, что готов заплатить 1495 долларов за open access, но все равно они отвергли, а теперь хотят опять рассмотреть статью. Но я решил, что после этого будет слишком, если я буду опять пытаться заплатить 1495 долларов: из-за их тупых догм они вначале отказались, а теперь, вроде бы, опять не против получить эти деньги. Поэтому написал им такой ответ:

Letter reference: HAA01

Dear Editors,

I am grateful that you have reconsidered your decision to immediately reject my paper. I thought about your request to confirm that I agree if you continue processing my paper. However, my decision is that I will not try to publish my paper in JPCO. I don't know whether or not you are interested in my reasons but they are described below.

First about me. I graduated from the Moscow Institute for Physics and Technology, got PhD from the Institute of Theoretical and Experimental Physics in Moscow and Dr. Sci. Degree (in Russia there are two doctoral degrees) from the Institute for High Energy Physics also known as the Serpukhov Accelerator. In Russia I worked as a leading scientist at the Joint Institute for Nuclear Research (Dubna, Moscow region) but in the US I work at a software company.

I gave talks at many international conferences, have many papers published in known journals on physics and mathematical physics (Annals Phys., Finite Fields and Applications, J. Math. Phys., J. Phys. A: Mathematical and Theoretical, Nucl. Phys. A, Phys. Lett., Physics of Particles and Nuclei, Phys. Rev. C and D, Phys. Rev. Letters, Theor. Math. Phys. and others) and 44 papers in arXiv.

My experience is that when I sent to known journals papers done in the framework of more or less mainstream approaches then typically such papers were accepted without problems. However, when a paper was based on non-mainstream approaches then great problems arose. This was not because the editors could say something specific or refute my results. Typically, they even did not understand what the paper was about, but they saw that the paper was not based on what was sacred for them.

The editorial policies of known journals are typically very impressive. However, when I dealt with those journals then typically it became obvious that the referees and board members did not feel obliged to follow those policies, they thought that they know better what papers should or should not be published and the referees often even did not understand that it was disgraceful to write a negative report if they understood nothing in the paper.

For example, I have five papers published in JPA, the last of them was published in 2004. All those papers have been done in frameworks of more or less mainstream approaches. The referee reports were very professional and helped to improve the papers. For example, in the last case there were two referee reports, positive and negative, the adjudicator advised in my favor, and this is a reasonable situation. However, all my next submissions to JPA have been rejected without any explanations, and nobody tried to understand my results. Typically, they sent me the same standard text as you sent on Sep 26th that"…articles must be of high scientific quality and be recognised as making a positive contribution to the literature. Your Paper has been assessed and has been found not to meet these criteria." So, in fact the statement is that my paper is not of high scientific quality and does not make a positive contribution to the literature. Scientific ethics implies that any negative statement should be substantiated but in all those cases no explanations have been given, and the phrase that the paper has been assessed gives no info on how it has been assessed.

For me it's interesting whether the editors understand that their actions contradict scientific ethics. I propose papers where quantum theory is based not on complex numbers but on finite math. I explain that my approach is more fundamental than standard one and moreover I have rigorously proved that standard quantum theory is a special degenerate case of quantum theory based on standard math. I have no doubt that my papers are fundamental and sooner or later (rather later than sooner) this will be acknowledged. My observation is that majority of physicists do not have even very basic knowledge in finite math. This is not a drawback because everybody knows something and does not know something, and it's impossible to know everything. I believe the mentality of physicists should be such that in physics different approaches should have a right to compete. However, the mentality of many physicists is such that if they don't understand something then this should not be published. My observation is that when physicists see that my papers are based on finite math then they immediately conclude that this is philosophy, pathology, exotics etc. and contradicts their dogmas (although, as I noted, typically they do not have even very basic knowledge in finite math).

When JPCO was created I was impressed by its editorial policy. The policy says that JPCO differs from other journals, that it «does not make a subjective assessment on the potential future significance of a paper, instead providing a rapid platform for communicating research that meets high standards of scientific rigour and contributes to the development of knowledge in physics». However, my experience with two papers shows that at least in my case the editors do not feel obliged to follow the editorial policy. They do not understand that my papers give FUNDAMENTAL contributions to the knowledge in physics. Therefore, the papers not only fully satisfy the JPCO policy but should be welcome by the editors. The most plausible explanation of such a situation is that when they see the words «finite mathematics» then their intention is to reject the paper right away and probably for them a strong argument in favor of their belief is that I am not from a university. It seems to me that the mentality of all editors should be such that they should welcome nonstandard approaches because this will make their journals more attractive. Especially, in view of the JPCO policy, this should be the case for the editors of JPCO. However, I see that the editors of JPCO have the same mentality as the editors of many other journals and if a submitted paper is not in mainstream then the paper has no chances to be published.

You acknowledged that the treatment of my paper was not fair because it had been commissioned. However, even if it had not been commissioned your response contradicts your policy and scientific ethics. So the fact that you have reconsidered your decision does not mean that mentality of the editors has been changed. In view of this situation, I think that if I agree that you continue processing my paper then the most probable scenario is the following. Probably you will not find referees who have even very basic knowledge in finite math and the mentality of majority of physicists is that if they do not understand something (e.g., if the words "finite mathematics" contradict their dogmas) then probably they will write a meaningless referee report with the advice to reject the paper. They will not care that their treatment of the paper contradicts the editorial policy and scientific ethics. In view of my experience, for editors this will be a good pretext to reject the paper. According to your policy, the authors have a right to appeal the decision. However, my experience with the first paper shows that all my arguments that the reports contradict the editorial policy and scientific ethics will not be taken into account and the appeal will not be considered. Since I am not young and do not want to have additional negative emotions, I have decided not to try to publish my paper in JPCO.

Sincerely, Felix Lev.

Следующая попытка: Taiwanese Journal of Mathematics. Их ответ был такой:

We do not have a full referee report, but quick opinions gathered suggest that it would be difficult to convince the editorial board to accept the article. Therefore, rather than begin a refereeing process that could take months, I am returning your manuscript to you now so that you have the chance to submit it elsewhere without delay.

Не буду комментировать этот ответ, но, во всяком случае, ответили через два дня и на том спасибо.

Еще одна попытка: Notre Dame Journal of Formal Logic. Ответа не было больше месяца и спросил о статусе:

Dear Professor Pillay,

The status of my paper is “With Editor” from November 6th, i.e. the paper is with the Editor for more than a month. I understand that the Editor is very busy. On the other hand, the paper is short (10 pages) and in my understanding rather simple. My understanding is that the paper is under review, right? Could you, please tell me when (even very approximately) the referee reports are expected.

Thank you. Sincerely, Felix Lev.

Т.е., по наивности я думал, что раз назначен редактор, который держит статью больше месяца, то статья на рецензии. Но в течение менее часа получил такие ответы от главного редактора:

Dear Felix,

The Editor-in-Chief on the philosophy side (Mic Detlefsen) died in October. We have appointed a replacement who will take over his papers. There are papers submitted in July which have not been dealt with yet.

Anand Pillay (Editor-in-Chief)

Dear Felix,

Actually I took the opportunity to look at your paper myself, and I can say quickly that it is not suitable for the Notre Dame Journal. The statement about $Z$ and the $Z/pZ$ (i.e. $F_p$) is obvious. (Also if you are interested there is a big literature about «pseudofinite» structures in logic. Easily found on google.)

So I will reject the paper.

Regards,

Anand Pillay

Dear Felix,

As I said in the email to you I am rejecting the paper. Sorry.

Anand PillayEditor-in-ChiefNotre Dame Journal of Formal Logic

Т.е. в первом ответе он как бы оправдывается, что из-за того, что бывший главный редактор, отвечающий за философию, умер, многие статьи задерживаются. Во-первых непонятно, почему он решил, что моя статья относится к философии. И непонятно, если статус был “With Editor”, то какому редактору послали. Ведь явно не тому, который умер, а тогда непонятно зачем он оправдывается. Но второй ответ пришел через 40 минут. Т.е., за эти 40 минут он посмотрел статью и решил отвергнуть. Из его ответа ясно, что до этого никто статью не смотрел, несмотря на статус “With Editor”. А третий ответ пришел через 5 минут.

Из его ответа ясно, что он статью не понял и не пытался понять, и, скорее всего, он не в состоянии понять. Я послал ему такое письмо:

Thank you for the info about your decision on my paper. I will not appeal the decision. However, let me note that when I send a paper to a journal, I am interested not only whether the paper will be accepted or not but also in knowing the opinion of qualified referees.

In fact, you were my referee and my understanding is that, although the formal status was “With Editor” for more than a month, nobody looked at the paper till Dec 10th, when it took you less than 40 minutes to come to the conclusion. From the formal point of view the reason of rejection was “The statement about Z and the Z/pZ (i.e. Fp) is obvious.” And also you advise me to look at the literature on «pseudofinite» structures. I would be very grateful if you answer the following questions.

I understand that the statement is simple, have no doubt that for you the statement is indeed obvious and several mathematicians said the same. However, in my understanding, in mathematics the statement that something is obvious needs to be explained. Could you, please give me a direct reference where this statement is proved and how the limit is understood. You and several mathematicians told me that this is obvious from ultraproducts, «pseudofinite» structures etc. and I agree. However, those notions are rather sophisticated. My paper is titled “A new look at potential vs. actual infinity”. Those notions are discussed in the framework of actual infinity. The mentality of many mathematicians is that problems with characteristic 0 are fundamental while finite rings or fields can be used as something auxiliary for tackling those problems. My observation is that the majority of mathematicians do not care that standard mathematics has foundational problems (as follows e.g. from Gödel's incompleteness theorems and from other considerations). My hope was that NDJFL does care about this.