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

starting with the rings Z/pZ, instead of Z (Peano arithmetic). This may be the case, but such an undertaking would take an enormous amount of work and, in my opinion, even if successful it will have little bearing on modeling nature. As I said, no mathematics is off limit if it's relevant in description of nature, and there is no need to rebuild the foundations for this purpose.”

In my paper and the last letter, I note that (during the last 80 years) there is a great problem that, by using the existing mathematics, physicists cannot construct a quantum theory which is mathematically consistent and can explain many existing experimental data. This is acknowledged by famous scientists and even Nobel Prize laureates (as I noted, even one of them wrote a paper titled “Living with Infinities”). Also, many authors and even some Nobel Prize laureates wrote papers conjecting that the ultimate quantum theory will be based on finite mathematics. Of course, constructing such a theory would take an enormous amount of work. However, in your opinion “, even if successful it will have little bearing on modeling nature” and “there is no need to rebuild the foundations”.

So, you do not know about existing fundamental problems, do not have ideas how to solve them, the opinion of famous scientists is not important to you, but your opinion is that “there is no need to rebuild the foundations”. So, your remarks are like those from the known Chekhov’s story “Letter to a learned neighbor” when a man writes to his neighbor: “You say that there are spots on the Sun; this cannot be because this can never be”.

You note that there are even similarities between our approaches because both start from a discrete approach. You will probably be indignant if someone, without any attempt to figure it out, says that your results are only declarations. You will probably say that you already have recognized works on this topic and this topic is related to generally recognized problems. But I can also say that I have papers in so-called prestigious journals, there are many other papers on this topic, and even Nobel Prize laureates wrote about this.

In summary, you asked me a question, I tried to answer this question in detail, there are no sign that you and the referee read my arguments and/or were able to understand them, but you say that my paper “is essentially just a declaration”. Giving negative statements about my arguments without any explicit mentioning them, contradicts scientific ethics and is simply indecent. I understand your last letter such that you do not want to spend any time on our discussion, and I also think that your attitude is such that any further correspondence is meaningless.

I wish all the best to you and your journal. Felix.

P. S. Your statement that “both the Galilean and the Lorentz transformations are parts of mathematics on equal footing” is not correct. As explained in the famous Dyson’s paper “Missed opportunities” published in 1972 in Bull. Amer. Math. Soc., the Lorentz group is more general than the Galilei one because the latter can be obtained from the former by contraction c→∞. In turn, being semisimple, the Lorentz group (it is more correct to talk about its covering group SL(2,C)) has a maximal possible symmetry and cannot be obtained from a more symmetric group by contraction. And, as I tried to explain in the paper, finite mathematics is more general than classical one because the latter can be obtained from the former by contraction p.

Как обычно, я привожу эту длинную переписку, понимая, что вряд ли кто-то захочет всю ее читать. Но я должен привести эту переписку, чтобы не сказали, что я тенденциозен, утверждая, что рассмотрение моей статьи не соответствовало ни editorial policy ни научной этики. Действительно, Сергей Табачников пишет, что мои утверждения unconvincing и что мои аргументы – только declaration.

Не знаю, понимает ли он, что такие утверждения без всякой попытки обосновать их, противоречат научной этике. И еще, как я пишу в своем ответе, его слово "criticism" не соответствует своему значению. Определение "criticism" такое: "the expression of disapproval of someone or something based on perceived faults or mistakes". То есть, предполагается, что даны какие-то аргументы. А его письма не содержат никакого намека, что он хоть в чем-то пытался разобраться. И рецензия тоже показывает, что, как я отмечаю, рецензент даже не прочитал внимательно статью. Вначале он пишет, что ему интересен ультрафинитизм, потом пишет, что реально можно что-то посчитать только с действительными числами, а если не так, то должны быть аргументы. Но весь смысл статьи, чтобы привести такие аргументы и, похоже, он этого даже не понял.

Моя следующая попытка – Archiv der Mathematik, и ответ Editor-in-Chief Ralph Chill такой:

"…We are aware of your having discussed this paper with Clemens Heine, and we have valuated the paper by ourselves. It is true that the paper is of general nature, and could be of interest for a broader audience, but we feel that the paper does not fit into this particular journal. We want to encourage you to submit your paper to a another journal, where it certainly will find its place…

То есть, он признает, что "It is true that the paper is of general nature, and could be of interest for a broader audience… ". То есть, он фактически признает, что статья полностью соответствует editorial policy. Но, почему-то, "but we feel that the paper does not fit into this particular journal". И он ведь математик, а не поэт, поэтому когда он апеллирует к своим чувствам, то это странно. Казалось бы, вопрос очень простой: соответствует статья editorial policy? Да или Нет? Ясно, что я написал appeal, но он на него не ответил. То есть, опять-таки, он, наверное, не понимает, что такой ответ противоречит научной этике.

Моя следующая попытка – Expositiones Mathematicae. Их editorial policy такая:

Our aim is to publish papers of interest to a wide mathematical