полная версия

Феликс Лев
Популярно о конечной математике и ее интересных применениях в квантовой теории

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 This is a rare occurrence and we apologise for any inconvenience the delayed and ultimately withdrawn article caused.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 Rowley

Editorial 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 Pillay

Editor-in-Chief

Notre 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. F_p) 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.

My math professor was a famous mathematician M.A. Naimark, and I was very impressed by his lectures on calculus and group representations. As I note in the abstract, the technique of standard math involves only potential infinity while the basis does involve actual infinity: the theory starts with Z, then rational, real, complex numbers and sets with different cardinalities are introduced etc. As a rule, in mathematics legitimacy of every limit is thoroughly investigated but in standard math textbooks it is not even mentioned that Z is the limit of Z/p (by the way, Z/p=F_p only if p is prime) and nothing is said on whether the limit is legitimate. The matter is that when Z/p is replaced by Z we arrive at standard math which has foundational problems.

I came to my ideas from physics where I proved that quantum theory based on finite math is more fundamental than quantum theory based on standard math: the latter is a special degenerated case of the former in the formal limit p→∞, and in my paper I argue that analogously, standard math is a special degenerate case of the former in the formal limit p→∞.

So I believe that the fact that Z/p→Z when p→∞ should be proved without reference to ultraproducts, «pseudofinite» structures etc. but directly by analogy with the proof that some sequence (a_n)→∞ when n→∞. Unfortunately, this is not easily found in google and the majority of mathematicians prefer to work with Z from the beginning without caring whether or not Z is a limit of a finite set.

Основной смысл письма такой: в математике не должно быть аргумента, что просто что-то очевидно. Любое утверждение, что что-то очевидно должно доказываться или объясняться. И получил в ответ два письма написанные с интервалом 22 минуты:

I am not saying that your Statement 1 follows from some machinery such as ultraproducts, I am just saying that Statement 1 is obvious. Given integers a, b for all stuff. large primes p, a+b, a·b in Z coincides with a+b, a·b in F_p.

Let me clarify. It is not just obvious it is a matter of definition. For a prime p, the field F_p consists of elements 0,1….,p-1, with addition and multiplication modulo p. Namely for a, b in F_p, a+b (in F_p) is the remainder when a+b is divided by p. Likewise for a·b. So by definition, if a,b are in F_p, then for p bigger than max of a+b, a·b, a+b and a·b coincide in Z and in F_p.

Т.е., вначале он пишет, что это очевидно и пытается объяснить. А через 22 минуты уже пишет, что это не только очевидно, но и является определением.

Я написал большой ответ:

I am disappointed with the treatment of my paper at NDJFL. For more than a month the status was “With Editor”, and my naïve expectation was that somebody is reading the paper. However, only after my query you spent 40 minutes or less and the only reason of rejection was “The statement about Z and the Z/pZ (i.e., F_p) is obvious”. In mathematics the statements that something is obvious should always be explained but I thought that since Editor-in-Chief of such a prestige journal makes such a statement then maybe indeed it is extremely obvious, and I don’t understand something trivial. That’s why I wrote that I would be very grateful if you explain your words. However, I was amazed by your response.

In the first email you continue to state that Statement 1 is obvious: “Given integers a, b for all stuff. large primes p a+b, a·b in Z coincide with a+b, a·b in F_p” (probably “stuff.” is a misprint of “sufficiently”) but after 22 minutes you wrote another email:

“Let me clarify. It is not just obvious it is a matter of definition. For a prime p, the field F_p consists of elements 0,1….,p-1, with addition and multiplication modulo p. Namely for a,b in F_p, a+b (in F_p) is the remainder when a+b is divided by p. Likewise for a·b. So by definition, if a,b are in F_p, then for p bigger than max of a+b,a·b, a+b and a·b coincide in Z and in F_p.", so now you are saying that this is the matter of definition.

 

My first remark is technical. The problem deals only with rings and has nothing to do with division. So, it is not necessary to consider the field F_p and only primes. The problem is whether Z is the limit of rings R_p=(0,1,…p-1) (with operations modulo p) when p→∞.

Again, in mathematics, mathematical statements should be formulated unambiguously such that different interpretations should be excluded. For this reason the words “for any” and “there exist” are often used in mathematical statements. However, saying about a and b you are not using those words, and one can only guess what you mean. Consider you “definition” “So by definition, if a,b are in F_p, then for p bigger than max of a+b,a·b, a+b and a·b coincide in Z and in F_p.” literally. For example, if a=0 and b=0 then for p > 0, a+b and a·b coincide in Z and in F_p. Or if a<10 and b<10 then for p > 100, a+b and a·b coincide in Z and in F_p.”. So your “definition” is indeed obvious.

I guess that probably you meant something like this: for any p₀ there exists a set S such that for any a+bϵS,a·b ϵS, a+b and a·b coincide in Z and in F_p for any p >= p₀, and card(S)→∞ when p₀→∞.

However, even if my guess is correct, this still cannot be a correct definition that R_p→Z when p→∞. The definition should be such that not only for two elements from S their sum and product coincide in Z and in R_p but that it is possible to find a number n such that for any m<=n the result of any m operations of multiplication, summation or subtraction of elements from S should be the same in Z and in R_p, and that n→∞ when p→∞.

The exact formulation of the definition is given in my paper, and I prove that with this definition indeed R_p→Z when p→∞. As I said, the definition should be to some extent analogous to the definition that the sequence (a_n) →∞ when n→∞: for any M>0 there exists n₀ such that a_n>=M for any n>= n₀.

I asked several mathematicians to give me a reference where this is proved but nobody gave such a reference. The response of some of them was analogous to yours: this is obvious. Then I asked that if this the case then why in mathematical textbooks this is not even mentioned and standard math starts from Z from the beginning, but again no response. As I wrote, they don’t care that standard math has foundational problems (as follows e.g. from Gödel’s incompleteness theorems and other considerations). But when I asked Prof. Zelmanov (who is the Fields Medal laureate) he did not say that this is obvious and advised me to look at Terence Tao’s blog where ultraproducts are considered. In my paper I thank Prof. Zelmanov for his advice and refer to the blog.

Technically indeed it is possible to prove that R_p→Z follows from the results on ultraproducts although in ultraproducts they consider only fields and their goal is to use finite fields for proving some features of fields of characteristic zero. Nevertheless, this is not a direct proof, and the construction is rather sophisticated.

In summary, I think that, with the probability 99.99 %, in the literature there is no direct proof that R_p→Z when p→∞ and so my proof is new. Let me note that my paper contains not only this result: I explain that this result is the first step in proving that finite math is more fundamental than standard one: the latter is a special degenerated case of the former in the formal limit p→∞.

However, it seems obvious that you even did not try to carefully read my proof and other results of the paper. You noticed that I prove that R_p→Z, immediately (within minutes) decided that this is obvious (as you say, even without the machinery of ultraproducts) and immediately wrote a rejection. I am amazed that the attitude to my paper at such a prestigious journal was on such a level.

For me it is not a great tragedy that my paper will not be published in NDJFL. I have no doubt that the results are fundamental, they will be acknowledged sooner or later and published elsewhere. However, I treat such an attitude to me as disgraceful from the professional point of view. Such an attitude in fact means that you treat me as unprofessional who submitted to NDJFL a junk which does not deserve consideration.

Of course you have a right to have such an opinion. However, if you think that your attitude was a mistake I would be grateful if you tell me this and will be fully satisfied. I understand that we are only people, everybody makes mistakes, you are very busy handling such a journal, you have to look at many papers and probably some of them are indeed junk, so probably mistakes in your work are inevitable. However, decent people acknowledge that they make mistakes when this becomes obvious.

В этом ответе вначале популярно объясняю, что его объяснения не имеют смысла. Пишу, что был очень удивлен, что в таком престижном журнале моя статья была рассмотрена на таком уровне.

В конце пишу, что для меня главное – не то, что статья не будет опубликована в его журнале, а то, что отношение к статье было позорным. Как будто я полностью не профессионален и послал в журнал мусор на который не стоит тратить время. Пишу, что все мы люди и ошибаемся, он очень занят с журналом, ему надо смотреть много статей и, наверное, часть из них мусор, так что, наверное, в его работе ошибок не избежать. Но порядочные люди признают, что делают ошибки когда это выясняется. И если он признает, что ошибся, то я буду удовлетворен.

По моим понятиям, любой ученый и тем более математик должен признать, что он неправ когда ему это объясняют. Допустим, что он решил, что мой ответ не очень вежливый. Но, по моим понятиям, когда главному редактору объясняют, что отношение к статье и автору было хамским и что он написал ответ совершенно неправильный с математической точки зрения, то любой порядочный ученый должен извиниться и, по меньшей мере сказать, что все будет пересмотрено. Я на этом не настаивал, а всего лишь попросил, чтобы он признал ошибку и что тогда я буду полностью удовлетворен. Но он даже не ответил, что показывает, что его какие-либо моральные проблемы не волнуют.

Еще одна попытка: Israel Journal of Mathematics. Первый ответ был обычным:

Unfortunately your paper is out of the scope of the Israel Journal of Mathematics. Therefore we cannot consider it for publication. we do thank you for considering our journal.

Sincerely yours,

Tamar Ziegler

Editor in Chief

Israel Journal of Mathematics

Т.е., отклоняют статью, якобы, потому что она не в теме журнала. Но описание редакционной политики журнала такое: “The Israel Journal of Mathematics contains high-quality research papers on {\bf all} aspects of mathematics and theoretical computer science”. Т. е. пишут, что журнал рассматривает статьи высокого качества по всем темам математики. Поэтому статью нельзя отклонить с предлогом, что она не по теме; единственной причиной отклонения может быть только то что статья низкого качества. А это уже значит, что должна быть рецензия, где показано, что статья действительно низкого качества. Но когда я им это написал, то ответ был такой:

The Editorial Board had a look at your paper and decided that the Israel Journal of Mathematics is not the right place for it. Therefore we will not further consider the paper. This decision is final.

Т.е., теперь они говорят, что редколлегия смотрела и решила, что их журнал – неподходящее место для статьи. А почему – никаких объяснений. И еще предупреждают меня, что это решение окончательное, чтобы я их больше не беспокоил. И плевать они хотели на научную этику.

Попытка опубликовать статью в European Physics Journal H.

Первый ответ опять стандартный:

Dear Dr Lev,

Thank you very much for having submitted your manuscript entitled:

Analogy Between Finite Mathematics and Special Relativity to The European Physical Journal H.

Your manuscript has been carefully considered by our Editorial Board, and it appears that your manuscript does not belong to the Aims and Scopes as specified at https://epjh.epj.org/epjh-aims-and-scope

Therefore, we regret to inform you that your manuscript will not be considered further for publication in The European Physical Journal H. We are sorry not to be able to bring you a positive outcome and hope that you will consider EPJH in a future occasion.

Yours sincerely, EPJH Managing Editors

Comments from the editors and reviewers: (и никаких… нет).

Мой ответ:

Dear Editors,

Thank you for your email informing about the editorial decision on my paper. The email says that " your manuscript does not belong to the Aims and Scopes as specified at https://epjh.epj.org/epjh-aims-and-scope". However, this link contains the following sentences:

"Contributions addressing the history of physics and of physical ideas and concepts, the interplay of physics and mathematics as well as the natural sciences, and the history and philosophy of sciences, together with discussions." I believe that my paper fully satisfies these requirements. So I would be grateful if your decision is reconsidered.

Thank you.

Sincerely, Felix Lev.

Ответ журнала: