While it is true that most on researchgate lack the knowledge required to give a proper evaluation of a newly presented hypothesis, most researchers are more excited to find someone who is both interested and knowledgeable in the subjects to which their theory/hypothesis reside in. Therefore, many researchers are eager to grab the opportunity to have their work examined when a hypothesis of a similar topic is presented, sort of like an informal peer review process. Additionally, it is difficult in general to find someone that is qualified and willing to give a paper a thorough review.

With kindest regard,

Edward

Edward,

My experience is that nobody dares to criticize another one's theory if it is well founded, but requires a deep mathematical knowledge to understand. The peer review mechanism does not work well for unorthodox and controversial theories. Most reviewers are strongly biased.

See: https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project#Initiator

Hans,

When I use the term peer review, I was using it from more of a figurative standpoint meaning that a researcher would read a paper and express their advice, criticism, and/or praise. As opposed to an actual peer review process, the direct interaction and presentation of a new hypothesis to researchers is indeed more conducive to the development of unorthodox and controversial theories. Furthermore, I do agree with your emphasis on the fact that many researchers show extreme trepidation or even avoid giving criticism on mathematically devout hypothesis. As such an action would show their inexperience and hinder other researchers from showing interest in their research. Either way, it's ultimately boils down to the fear of hurting one's reputation and their research endeavors.

I must offer that some more experienced and well-versed researchers May appreciate a well founded assertion, but will not lend any of their expertise whether it be praised or criticism openly due to the controversial nature of the theory or hypothesis. In these situations, I find that it's better to initiate private messages with researchers concerning your work. Although I must admit from personal experience that this can also be a taxing task.

P.s. I am going to follow link that you attached to this message.

Best,

Edward

@ Hans van Leunen

You are not right with criticism at all, as I think.

There was a good discussion about the counter-proof to Cantor (Could I have comments about my "Note on Cantor's diagonal argument"?).

There is a long discussion about consciousness (Can we mathematically model consciousness?).

Or did I misunderstand you?

Let´s give a good example and have a discussion on my (I hope well founded and easy understandable) new theory of algebra.

My (proved) statement: `Mathematicians only can count but they are not able to calculate!´. Neither to discuss this thesis. Could you (my thesis depends on physics, not mathematics)?

With kind regards, Peter

Dear Peter Kepp,

It is proper to spend attention to the simple operations in sets and number systems. Many good math books cover these operations. In physics these number systems play interesting roles in areas that are not so well documented. For example, how does a set change when it passes from a countable set to a continuum. Or what is the influence of dimension in a multidimensional number system. The arithmetic capabilities decrease when the dimension increases. Dimension alone does not determine the arithmetic capabilities. A rule determines how addition and multiplication transfer to higher dimensions. What most people forget is that multidimensional number system exist in different versions that differ in the way that coordinate systems can sequence them. These characteristics are important, because Hilbert spaces can only cope with number systems that are normed division rings. Nature appears to exploit these facts. If you know enough about number systems, then you can understand many facts that are mysterious to most scholars. For example, electric charges and color charges are directly related to the fact that quaternionic number systems exist in many versions that differ in their symmetry properties and their chirality.

Look at the corresponding chapters of the Hilbert Book Model Project.

https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project#Quaternions

@ Hans van Leunen

Sorry, but you haven´t had any look on my papers or you didn´t understand anything.

A discussion in that way just is so as you qualified all discussions here.

If the definition of a group fails, so also for the upper classes (half-ring, ring and field). Quaternions don´t make it better. We have to discuss the basics!

For to do physics we have to use a true (isometric) number- and calculation-system. But not doing physics following any disproved nonsense in math.

Peter, I scanned over your papers.

If you google for groups, fields and rings, then you find many entries from well known universities.

I consider these algebraic constructs as basic mathematics and this stuff is well covered in many mathematical text books. I agree that these basics play an essential role and are important. But the less well known aspects of arithmetic that occur in higher dimensional number systems and the interaction between discrete sets and continuums play a more essential role in the comprehension of what happens in the lower levels of the structure of physical reality. These aspects are not part of the regular university lectures. That is why only a few mathematicians dive into these peculiarities. Most physicists do not even dare to go that deep.

If you understand these subjects, then please explain why the embedding of a separable Hilbert space into a non-separable Hilbert space may involve stochastic processes. For me this is the biggest mystery of reality.

Dear Hans van Leunen,

thanks for your answer. But I didn´t need to google groups, rings and fields. I disproved that all after a very deep study to that at a series of lectures by Conrad Kuck.

Numbers do have two meanings. They could name the place of an ordering or, in mathematical (calculating) meaning, be the number (of amount).

No number — ever — has it´s own dimension.

The quantities we handle by mathematics have to depicted by three parts:

Number (of amount), measure, unit.

Quaternions seem for me to be equivalents for four-dimensional vectors.

I don´t have any time for to study such topic because I believe that the Hilbert Space is completed by three dimensions.

Physics leads to examine expressions (qualities) like energy which contain more than three factors (divisors). Mathematical constructs, like the quaternions may help to handle physical expressions with a higher degree of factors.

I will stay at my reform. Sorry for your topic.

Regards, Peter