I wrote in another thread
Looking through the cited bibliography in the paper to be reviewed I noticed that my own paper about quantum fractals on hyperspheres is being quoted, so I started to feel a sympathy towards the authors. Who of us does not like to be quoted, right? So I started reading the paper with a positive attitude.
At the beginning the reading was easy. A little error here, a small correction there. Every referee likes these small errors because pointing them out does not take much time and, on the other hand, serves as a proof that the referee has indeed read the paper. Some smart authors, those who are aware of referees' psychology, are making such small errors on purpose – to make the referee happy and to encourage him/her not to look in the paper any deeper!
I was thinking a little bit about what can be the use of random walk on hypercubes, but the authors remarked that it can be used in studies of error propagation. Other well established authors studied similar mathematical problems before, so the subject matter of the paper has been sanctioned this way.
As I said above, the start was easy, yet pretty soon I found something that caused me to frown. There was a formula that should not be there, since it was taken from another paper and this other paper dealt with an essentially different case, based on a different set of assumptions. So I highlighted the formula in red and continued reading. Is this formula important for the final results of the paper? It often happens that we are getting right results using wrong methods. Perhaps this is the case here? But then, on page 9, I noticed that this suspicious formula is indeed being used. Here is this page:
and the suspicious term is the last term in the first equation from the top. The full page in pdf format is here.
Scary, isn't it? To check the calculations would take me a full month. What to do? First, I thought, I will do a computer simulation using random number generator. If my simulations will give the results that are evidently contradictory to the final results of the authors, then I will return the paper for corrections. If, on the other hand, my simulations will be in agreement with the results of the paper, then I will conclude that the authors, even if they are sinners, know what they are doing and so their sins can be forgiven.
Yet, after some thinking, I realized that to do the simulations would take me probably two weeks. Why should I do it, I was thinking. And then I remembered this phrase from the Bible “Unto a stranger thou mayest lend upon usury” (Deut. 23.20). Eureka! I will suggest, instead, that the authors should do the simulations, which should not be too difficult for them as I knew that they did similar simulations before. And, with this insight, I wrote my referee report. After listing of all the little errors and inexactitude that I noticed I added the following final suggestion:
This time two of the authors were from India and one from China. The subject was also more exotic. It involved octonions (which for mathematicians are much like octopuses), spinning masses, magnetic monopoles, gravi-magnetism and more of such really scary things. A whole Halloween zoo. This time I really got scared as the authors were referring to at least six other their previous papers published in some obscure journals. What to do?
So I wrote to the editor of the journal asking him to kindly ask the authors to provide me with copies of their previous works. They kindly did. The subject matter happened to be in my domain of expertise. I have discussed few years ago the subject of gravi-magnetism with the chief scientist at ESA, European Space Agency located in Paris. So I skipped the exotic octonion part and moved to the real meat – the EQUATIONS. Well, there was nothing new in the equations, I knew them. What was new was the lousy way they were presented and described in the paper! To make the long story short, I will disclose now my sweet and short final report:
And, lo and behold, just a few days ago I got a chance to add to these “serious flaws” another flaw, this time one due to myself! At the end of August I the editors of a professional specialized journal „Markov Processes and Related Fields” asked me to serve as a referee of a certain paper. One of the authors was an American mathematician, whom I met a few years ago at a conference, the second one, French, from Laboratoire de Recherche en Informatique et ses Applications, whom I did not know. I have had a look at the paper, and put it in a drawer – for later. Usually the editors give a couple of months for a review... But then I have suffered from the hard drive failure, I had to finish my own paper (still waiting to be finished ... ) and also there was the work on publishing of the proceedings of a conference that was held a couple of years ago and that the Springer publisher is waiting for .... so I have forgotten about “Markov processes and related fields”. But when two weeks ago I received from the Chief Editor of the journal a kind and polite remainder, willy-nilly I recovered the paper to be reviewed and started to study it. As it happens the paper is based on a previous paper by one of the authors, so I had to read it first. It deals with “random walks on hypercubes”. Hypercube, you know, is like an ordinary cube, but in four (or more) dimensions. The four dimensional hypercube is also known as the tesseract. Sacred geometry folks even think that contemplating tesseracts and si,ilar creatures takes us into a higher reality. I don't know. For me geometry is neither sacred nor scary – mathematics can effectively deal with hyperdimensional constructions even on the Halloween night!
Looking through the cited bibliography in the paper to be reviewed I noticed that my own paper about quantum fractals on hyperspheres is being quoted, so I started to feel a sympathy towards the authors. Who of us does not like to be quoted, right? So I started reading the paper with a positive attitude.
At the beginning the reading was easy. A little error here, a small correction there. Every referee likes these small errors because pointing them out does not take much time and, on the other hand, serves as a proof that the referee has indeed read the paper. Some smart authors, those who are aware of referees' psychology, are making such small errors on purpose – to make the referee happy and to encourage him/her not to look in the paper any deeper!
I was thinking a little bit about what can be the use of random walk on hypercubes, but the authors remarked that it can be used in studies of error propagation. Other well established authors studied similar mathematical problems before, so the subject matter of the paper has been sanctioned this way.
As I said above, the start was easy, yet pretty soon I found something that caused me to frown. There was a formula that should not be there, since it was taken from another paper and this other paper dealt with an essentially different case, based on a different set of assumptions. So I highlighted the formula in red and continued reading. Is this formula important for the final results of the paper? It often happens that we are getting right results using wrong methods. Perhaps this is the case here? But then, on page 9, I noticed that this suspicious formula is indeed being used. Here is this page:
and the suspicious term is the last term in the first equation from the top. The full page in pdf format is here.
Scary, isn't it? To check the calculations would take me a full month. What to do? First, I thought, I will do a computer simulation using random number generator. If my simulations will give the results that are evidently contradictory to the final results of the authors, then I will return the paper for corrections. If, on the other hand, my simulations will be in agreement with the results of the paper, then I will conclude that the authors, even if they are sinners, know what they are doing and so their sins can be forgiven.
Yet, after some thinking, I realized that to do the simulations would take me probably two weeks. Why should I do it, I was thinking. And then I remembered this phrase from the Bible “Unto a stranger thou mayest lend upon usury” (Deut. 23.20). Eureka! I will suggest, instead, that the authors should do the simulations, which should not be too difficult for them as I knew that they did similar simulations before. And, with this insight, I wrote my referee report. After listing of all the little errors and inexactitude that I noticed I added the following final suggestion:
End. Now I can return to my own paper, to make 100% sure that I will not make an error in my own work. But .... no. When I was putting back the paper into my file cabinet, I noticed that there is another paper there that is also waiting to be reviewed, for another journal, on another subject.
This time two of the authors were from India and one from China. The subject was also more exotic. It involved octonions (which for mathematicians are much like octopuses), spinning masses, magnetic monopoles, gravi-magnetism and more of such really scary things. A whole Halloween zoo. This time I really got scared as the authors were referring to at least six other their previous papers published in some obscure journals. What to do?
So I wrote to the editor of the journal asking him to kindly ask the authors to provide me with copies of their previous works. They kindly did. The subject matter happened to be in my domain of expertise. I have discussed few years ago the subject of gravi-magnetism with the chief scientist at ESA, European Space Agency located in Paris. So I skipped the exotic octonion part and moved to the real meat – the EQUATIONS. Well, there was nothing new in the equations, I knew them. What was new was the lousy way they were presented and described in the paper! To make the long story short, I will disclose now my sweet and short final report:
After sending this out I thought NOW I can return to my own paper. But no. Not so easy. As one of the German engineers thinks that he has discovered mysteries of gravity and electromagnetism that were overlooked by Maxwell, Einstein and their followers. Perhaps he indeed discovered them? So, I should help him to put his work in a form that will be understood by others. But this time I am not in a hurry, so I wrote to my German correspondent that I will not be able to devote to his problem more than an hour per day. Well, perhaps more .....
