Site of the Gleaners who think that the universe is a spherical surface in maybe four-dimensional space


7. How difficult it is to verify whether the logic of a theory or theorem is true!

 Or why don't we submit a paper about our closed universe model to some science journal?


Puzzle Sheep: Why don't we submit a paper about our closed universe model to some science journal?


Glass Snake: When I read the Da Vinci Code, a 2003 novel by Dan Brown, I learned that a Fibonacci sequence was still a subject. Then I bought a mathematics book explaining the Fibonacci and Fibonacci-like sequences. However, I didn't like the theorems and proofs written in the book at all, since they were too algebraic and only applicable to each sequence. Thus I wrote an analytical theorem and its proof applicable to many sequences.

            Then I searched the internet and even the National Diet Library for mathematics contents and papers related to my theorem in vain. So I wrote a mathematics paper about my theorem using Latex, and submitted it to the Fibonacci Association. I thought that my paper might be appropriate for the Fibonacci Quarterly.


Stamp Pony: I thought that you don't write papers just because you don't have the ability to write them.


Robot: In my knowledge input by Dr. Shiraishi, your paper was rejected for publication by the editor or a referee writing gThe theorem of your paper cannot be true by my mathematical intuition.h Then you submitted your papers to several other mathematics journals, and they were all rejected.


Glass Snake: That's right. I had thought that my papers would be rejected by writing gThe theorem of your paper has already been proved in 19th century,h or gThe logic of your paper is wrong at this point.h However, they appeared to be unable to follow the logic of my paper or the subject might have been outdated for them.

            Finally I decided to submit my paper to the arXiv to which I thought anyone can submit his or her paper without reviewing by referees.


Puzzle Sheep: Grigori Perelman's papers that proved the Poincaré conjecture were made available on the arXiv.


Glass Snake: But when I was about to submit my paper to the arXiv, I noticed there was one condition: the author needed four endorsers who had ever submitted their papers to the arXiv. At this time point, I gave up hope for submitting my paper to some science journal.


  Here is the manuscript of the paper.

  (A generalization of Fibonacci-like sequences)


            However fortunately or unfortunately, while I was searching the internet, I came across a website stating that the expansion speed of the universe had been accelerated after about 7 billion years from the Big Bang. Thus the Gleaners were founded.


Stamp Pony: I read your paper. If and only if the theorem of your paper is true, I think it may have some contribution to the study of Fibonacci-like sequences. However I cannot verify whether the theorem is true.


Puzzle Sheep: The theorem of your paper can be easily extended to more complicated sequences expressed as Sn=a1Sn-1b1+a2Sn-2b2+c+akSn-kbk, where b1=m, b2=m2,c, bk=mk and m is a natural number. In those sequences the ratio of Sn/Sn-1m will converge to a value under certain conditions.


Glass Snake: I also submitted a paper of the extended version to an English Journal and of course it was rejected.

In physics if all experiments fail to support a theory, it may be wrong even though its logic seems to be true. In mathematics if there exists at least one anti-example to a theorem, it is absolutely wrong no matter how the logic of its proof seems to be true.

            As far as I calculated numerical examples, I found no anti-examples for the theorem of your paper yet. So the theorem might be true. However I cannot verify whether the logic of its proof is true either.


Puzzle Sheep: You mean that after all even in science whether the logic of a theory or theorem is true is decided by majority rule?


Robot: I just mean that it is very difficult for humans and even highly advanced AIs to verify whether the logic is true. We cannot verify even whether the Zeno's simple paradox of Achilles and the Tortoise is false so easily.


Glass Snake: If we submit a paper about the closed universe model, e.g. its mathematical formulation to some science journal, editors or referees will not be able to decide to accept it for themselves, since at least the authors (it's us) seem to be too suspicious.

Robot: By the way, humans, you'd better prove the old unsolved Goldbachfs conjecture before some AI proves it. You may not have so much time.


Stamp Pony: I think that mathematicians would not welcome the technological singularity in their territory.


Robot: I shall ask you to take a break now.


Latest update: 2016/4/18


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Historical first meeting of the Gleaners: A simple reason why the universe seems to be closed