by gill1109 » Tue Dec 22, 2020 12:21 am
Joy Christian wrote:Joy Christian wrote:.
A professor of Engineering and Computer Science from a well-known Canadian University has taken an active interest in my "octonian-like" paper that Gill had campaigned to have retracted from the journal
Communications in Algebra. Here is the abstract of the professor's paper, which he has written with one of his Ph.D. students:
Using elementary linear algebra, this paper clarifies and proves some concepts about the previously introduced octonion-like associative division algebra (pseudo-octonion algebra). For a specific seminorm described in the paper (which differs from the norm used in the original paper), it is shown that the pseudo-octonion algebra is a semi-normed algebra, which does not contradict Hurwitz’s theorem. Moreover, additional results related to the computation of inverse numbers in the pseudo-octonion algebra are introduced in the paper, confirming that the pseudo-octonion algebra is a division algebra with no zero divisors using the seminorm. The elementary linear algebra descriptions also allow straightforward software implementations of the pseudo-octonion algebra.
I have read his paper, but it is not yet available online. I will post a link here when it becomes available. My original paper is available on the arXiv:
https://arxiv.org/pdf/1908.06172.pdf.
I have posted Gill's retraction saga (involving John C. Baez) on PubPeer for the future historians and sociologists of science:
https://pubpeer.com/publications/E3CC09 ... 5CAEE98D#5.
The paper has now appeared online:
https://arxiv.org/ftp/arxiv/papers/2012/2012.11359.pdf.
.
Notice that they do not use Christian’s norm, but introduce a *semi-norm*, in other words, non-zero elements can have norm zero. If one now follows the usual mathematical procedure of forming equivalence classes of all elements at zero distance to one another, the result will be a collapse of dimension. The space with this “norm” reduces to the quaternions. After all, it’s an associative normed division algebra, and the Hurwitz theorem says it must be R, C or H. It’s overparametrised. It’s actually only 4 dimensional.
[quote="Joy Christian"][quote="Joy Christian"].
A professor of Engineering and Computer Science from a well-known Canadian University has taken an active interest in my "octonian-like" paper that Gill had campaigned to have retracted from the journal [i]Communications in Algebra[/i]. Here is the abstract of the professor's paper, which he has written with one of his Ph.D. students:
[quote]Using elementary linear algebra, this paper clarifies and proves some concepts about the previously introduced octonion-like associative division algebra (pseudo-octonion algebra). For a specific seminorm described in the paper (which differs from the norm used in the original paper), it is shown that the pseudo-octonion algebra is a semi-normed algebra, which does not contradict Hurwitz’s theorem. Moreover, additional results related to the computation of inverse numbers in the pseudo-octonion algebra are introduced in the paper, confirming that the pseudo-octonion algebra is a division algebra with no zero divisors using the seminorm. The elementary linear algebra descriptions also allow straightforward software implementations of the pseudo-octonion algebra.[/quote]
I have read his paper, but it is not yet available online. I will post a link here when it becomes available. My original paper is available on the arXiv: https://arxiv.org/pdf/1908.06172.pdf.
I have posted Gill's retraction saga (involving John C. Baez) on PubPeer for the future historians and sociologists of science: https://pubpeer.com/publications/E3CC09191C99B14164303D5CAEE98D#5.
[/quote]
The paper has now appeared online: https://arxiv.org/ftp/arxiv/papers/2012/2012.11359.pdf.
.[/quote]
Notice that they do not use Christian’s norm, but introduce a *semi-norm*, in other words, non-zero elements can have norm zero. If one now follows the usual mathematical procedure of forming equivalence classes of all elements at zero distance to one another, the result will be a collapse of dimension. The space with this “norm” reduces to the quaternions. After all, it’s an associative normed division algebra, and the Hurwitz theorem says it must be R, C or H. It’s overparametrised. It’s actually only 4 dimensional.
