Site of the Gleaners who think that the universe is a spherical
surface in maybe four-dimensional space
(to the proofs of Goldbach's conjecture)
7. How difficult it is to verify whether the logic of a theory or
theorem is true! (to the revised part)
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unable to follow the logic of my paper or the subject might have been outdated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)
Fibonacci(generalization).pdf
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.
Here is the manuscript of the latter paper.
(Powered Fibonacci-like sequences.pdf)(added file)
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 Goldbachfs conjecture
before some AI proves it. You may not have so much time.
Stamp Pony:
I think that mathematicians would not wish to welcome the technological
singularity in their territory.
Glass Snake: You don't have to worry about the AI matter, because we have already proved
the Goldbach's conjecture.
Here are the theorems we have proved:
(added proofs)
<<proofs of Goldbach's conjecture.pdf>>
Theorem 1: Every positive or negative even integer is expressed
as the difference between two primes. Or every even integer n is expressed as p - q, where p and q are primes.
Theorem 2(Goldbach's conjecture): Every even integer greater than 2 is
expressed as the sum of two primes. Or every even integer n greater than 2 is expressed as p + q, where p and q are primes.
Lemma 1: Every positive or negative odd integer is
expressed as the addition and/or subtraction of three primes. Or every positive
or negative odd integer m is
expressed as p+q+r or p-q+r and so on, where p, q, and r are primes.
Proofs of those thorems are presented in the above manuscript.
Robot: Wow! You talk too big and live very humble! I don't know if the proofs
are right.
Puzzle Sheep: Anyway the die is cast. The Great Bull would have said "Humans might
have spent too much time to solve them."
Robot: Well done members! I shall ask you to take a break now.
cccccccccccc.
Robot:
Members, our tea break is over! Here we will go back to our main theme, namely to develop a warp navigation
system.
Stamp Pony:
It seems to me that the theme may be impossible to achieve for centuries.
Puzzle Sheep:
Not necessarily. As I have explained the variation of the Hubble constant in a second spin-off meeting, it was assumed that in the
vicinity of the earth, the time on S3 (the universe) passes faster than that on
the earth. What if we apply the assumption to for example a Trappist-1
mission?
Glass Snake:
Then it leads to that while for example one hundred years have passed for the
hibernating astronauts or waking astro-AIs of the
mission, only a few years may have passed for people on the earth.
Robot:
Fantastic! You mean that in the mission a conventional navigation system will
become a quasi-warp navigation system automatically.
Glass Snake:
Thatfs right. In short fortunately as for a space travel in the vicinity of the
earth we might already have built a quasi-warp navigation system.
Stamp Pony:
NASA announced that Voyager 2 had left the Solar System. So if we want to
verify the assumption (the time on S3 passes faster than that on the earth), we
have only to compare the time interval measured at Voyager 1 or 2 with that
measured on the earth. If the time interval measured at Voyager 1 or 2 is longer than that
measured on the earth, the assumption is right.
Puzzle Sheep:
If not, we have to fabricate another explanation.
Robot:
I shall ask you to close the meeting now.
All:
We are spherical-surfacebeings! We are the Gleaners!
Robot:
In Quark accent!
(Quark is a Ferengi businessman in the Star Trek Deep
Space 9)
All:
Good morning, we are the Gleaners! The Ferengifs
Rules of Acquisition No. 79: Beware of the Vulcan greed for knowledge!
Robot:
You, almost genuine surfacebeings! Mission
accomplished! Dismissed!
Latest update: 2019/11/09
A narrow and maybe insecure path to the Gleaners:
(Mail to: o-pat-consulting@hotmail.co.jp)
Historical first meeting of the Gleaners: A
simple reason why the universe seems to be closed