# Sometimes an anonymous review is “a tale told by an idiot …”

… “full of sound and fury, signifying nothing.” And the editor believes it, even if it is self-contradictory, after sitting on the article for half a year.

There are two problems:

• the problem of time; you write a long and dense article, which may be hard to review and the referee, instead of declining to review it, it keeps it until the editor presses him to write a review, then he writes some fast, crappy report, much below the quality of the work required.
• the problem of communication: there is no two way communication with the author. After waiting a considerable amount of time, the author has nothing else to do than to re-submit the article to another journal.

Both problems could be easily solved by open peer-review. See Open peer-review as a service.

The referee can well be anonymous, if he wishes, but a dialogue with the author and, more important, with other participants could only improve the quality of the review (and by way of consequence, the quality of the article).

I reproduce further such a review, with comments. It is about the article “Sub-riemannian geometry from intrinsic viewpoint” arXiv:1206.3093 .  You don’t need to read it, maybe excepting the title, abstract and contents pages, which I reproduce here:

Sub-riemannian geometry from intrinsic viewpoint
Marius Buliga
Institute of Mathematics, Romanian Academy
P.O. BOX 1-764, RO 014700
Bucuresti, Romania
Marius.Buliga@imar.ro
This version: 14.06.2012

Abstract

Gromov proposed to extract the (differential) geometric content of a sub-riemannian space exclusively from its Carnot-Caratheodory distance. One of the most striking features of a regular sub-riemannian space is that it has at any point a metric tangent space with the algebraic structure of a Carnot group, hence a homogeneous Lie group. Siebert characterizes homogeneous Lie groups as locally compact groups admitting a contracting and continuous one-parameter group of automorphisms. Siebert result has not a metric character.
In these notes I show that sub-riemannian geometry may be described by about 12 axioms, without using any a priori given differential structure, but using dilation structures instead.
Dilation structures bring forth the other intrinsic ingredient, namely the dilations, thus blending Gromov metric point of view with Siebert algebraic one.
MSC2000: 51K10, 53C17, 53C23

1 Introduction       2
2 Metric spaces, groupoids, norms    4
2.1 Normed groups and normed groupoids      5
2.2 Gromov-Hausdorff distance     7
2.3 Length in metric spaces       8
2.4 Metric profiles. Metric tangent space      10
2.5 Curvdimension and curvature     12

3 Groups with dilations      13
3.1 Conical groups     14
3.2 Carnot groups     14
3.3 Contractible groups   15

4 Dilation structures  16
4.1 Normed groupoids with dilations     16
4.2 Dilation structures, definition    18

5 Examples of dilation structures 20
5.1 Snowflakes, nonstandard dilations in the plane    20
5.2 Normed groups with dilations    21
5.3 Riemannian manifolds    22

6 Length dilation structures 22
7 Properties of dilation structures    24
7.1 Metric profiles associated with dilation structures    24
7.2 The tangent bundle of a dilation structure    26
7.3 Differentiability with respect to a pair of dilation structures    29
7.4 Equivalent dilation structures     30
7.5 Distribution of a dilation structure     31

8 Supplementary properties of dilation structures 32
8.1 The Radon-Nikodym property    32
8.2 Radon-Nikodym property, representation of length, distributions     33
8.3 Tempered dilation structures    34
9 Dilation structures on sub-riemannian manifolds   37
9.1 Sub-riemannian manifolds    37
9.2 Sub-riemannian dilation structures associated to normal frames     38

10 Coherent projections: a dilation structure looks down on another   41
10.1 Coherent projections     42
10.2 Length functionals associated to coherent projections    44
10.3 Conditions (A) and (B)     45

11 Distributions in sub-riemannian spaces as coherent projections    45
12 An intrinsic description of sub-riemannian geometry    47
12.1 The generalized Chow condition     47
12.2 The candidate tangent space    50
12.3 Coherent projections induce length dilation structures  53

Now the report:

Referee report for the paper

Sub-riemannian geometry from intrinsic viewpoint

Marius Buliga
for

New York Journal of Mathematics (NYJM).

One of the important theorems in sub-riemannian geometry is a result
credited to Mitchell that says that Gromov-Hausdorff metric tangents
to sub-riemannian manifolds are Carnot groups.
For riemannian manifolds, this result is an exercise, while for
sub-riemannian manifolds it is quite complicate. The only known
strategy is to define special coordinates and using them define some
approximate dilations. With this dilations, the rest of the argument
becomes very easy.
Initially, Buliga isolates the properties required for such dilations
and considers
more general settings (groupoids instead of metric spaces).
However, all the theory is discussed for metric spaces, and the
groupoids leave only confusion to the reader.
His claims are that
1) when this dilations are present, then the tangents are Carnot groups,
[Rmk. The dilations are assumed to satisfy 5 very strong conditions,
e.g., A3 says that the tangent exists – A4 says that the tangent has a
multiplication law.]
2) the only such dilation structures (with other extra assumptios) are
the riemannian manifolds.
He misses to discuss the most important part of the theory:
sub-riemannian manifolds admit such dilations (or, equivalently,
normal frames).
His exposition is not educational and is not a simplification of the
paper by Mitchell (nor of the one by Bellaiche).

The paper is a cut-and-past process from previous papers of the
author. The paper does not seem reorganised at all. It is not
consistent, full of typos, English mistakes and incomplete sentences.
The referee (who is not a spellchecker nor a proofread) thinks that
the author himself could spot plenty of things to fix, just by reading
the paper (below there are some important things that needs to be
fixed).

The paper contains 53 definitions – fifty-three!.
There are 15 Theorems (6 of which are already present in other papers
by the author of by other people. In particular 3 of the theorems are
already present in [4].)
The 27 proofs are not clear, incomplete, or totally obvious.

The author consider thm 8.10 as the main result. However, after
unwrapping the definitions, the statement is: a length space that is
locally bi-lipschitz to a commutative Lie group is locally
bi-lipschitz to a Riemannian manifold. (The proof refers to Cor 8.9,
which I was unable to judge, since it seems that the definition of
“tempered” obviously implies “length” and “locally bi-lipschitz to the
tangent”)

The author confuses the reader with long definitions, which seems very
general, but are only satisfied by sub-riemannian manifolds.
The definitions are so complex that the results are tautologies, after
having understood the assumptions. Indeed, the definitions are as long
as the proofs. Just two examples: thm 7.1 is a consequence of def 4.4,
thm 9.9 is a consequence of def 9.7.

Some objects/notions are not defined or are defined many pages after
they are used.

Small remarks for the author:

def 2.21 is a little o or big O?

page 13 line 2. Which your convention, the curvdim of a come in infinite.
page 13 line -2. an N is missing in the norm

page 16 line 2, what is \nu?

prop 4.2 What do you mean with separable norm?

page 18 there are a couple of “dif” which should be fixed.
in the formula before (15), A should be [0,A]

pag 19 A4. there are uncompleted sentences.

Regarding the line before thm 7.1, I don’t agree that the next theorem
is a generalisation of Mitchell’s, since the core of his thm is the
existence of dilation structures.

Prop 7.2 What is a \Gamma -irq

Prop 8.2 what is a geodesic spray?

Beginning of sec 8.3 This is a which -> This is a

Beginning of sec 9 contains a lot of English mistakes.

Beginning of sec 9.1 “we shall suppose that the dimension of the
distribution is globally constant..” is not needed since the manifold
is connected

thm 9.2 rank -> step

In the second sentence of def 9.4, the existence of the orthonormal
frame is automatic.

Now, besides some of the typos, the report is simply crap:

• the referee complains that I’m doing it for groupoids, then says that what I am doing applies only to subriemannian spaces.
• before, he says that in fact I’m doing it only for riemannian spaces.
• I never claim that there is a main result in this long article, but somehow the referee mentions one of the theorems as the main result, while I am using it only as an example showing what the theory says in the trivial case, the one of riemannian manifolds.
• the referee says that I don’t treat the sub-riemannian case. Should decide which is true, among the various claims, but take a look at the contents to get an opinion.
• I never claim what the referee thinks are my two claims, both being of course wrong,
• in the claim 1) (of the referee) he does not understand that the problem is not the definition of an operation, but the proof that the operation is a Carnot group one (I pass the whole story that in fact the operation is a conical group one, for regular sub-riemannian manifolds this translates into a Carnot group operation by using Siebert, too subtle for the referee)
• the claim 2) is self-contradictory just by reading only the report.
• 53 definitions (it is a very dense course), 15 theorems and 27 proofs, which are with no argument: “ not clear, incomplete, or totally obvious
• but he goes on hunting the typos, thanks, that’s essential to show that he did read the article.

There is a part of the text which is especially perverse: The paper is a cut-and-past process from previous papers of the
author.

Mind you, this is a course based on several papers, most of them unpublished! Moreover, every contribution from previous papers is mentioned.

Tell me what to do with these papers: being unpublished, can I use them for a paper submitted to publication? Or else, they can be safely ignored because they are not published? Hmm.

This shows to me that the referee knows what I am doing, but he does not like it.

Fortunately, all the papers, published or not, are available on the arXiv with the submission dates and versions.

______________________________________

See also previous posts:

________________________________________

# Academic Spring and OA movement just a symptom, not cause of change

… a reaction to profound changes which  question the role of universities and scholars. It’s a symptom of an adaptation attempt.

The OA movement, which advances so slowly because of the resistance of the scholars (voluntarily lulled by the propaganda machine of the association between legacy publishing industry and rulers of universities), is just an opening for asking more unsettling questions:

• is the  research article as we know it a viable vehicle of communication?
• what is the difference between peer-reviewing articles and writing them?
• should review be confined to scholars, or informed netizens (for example those detecting plagiarism) have their place in the review system?
• is an article a definite piece of research, from the moment of publishing it (in whatever form, legacy or open), or it is forever an evolving project, due to contributions from a community of interested peoples, and if the latter is the case, then who is the author of it?
• is it fair to publish an article inspired (in the moral sense, not the legal one) from information freely shared on the net, without acknowledging it, because is not in the form of an article?
• is an article the goal of the research, as is the test the goal of studying?

Which is our place, as researchers? Are we like the scholars of medieval universities, becoming increasingly irrelevant, less and less creative, with our modern version of rhetoric and theological studies, called now problem solving and grant projects writing?

If you look at the timing of the end of the medieval universities and the flourishing of the early modern ones, there are some patterns.We see that (wiki source on early modern universities):

At the end of the Middle Ages, about 400 years after the first university was founded, there were twenty-nine universities spread throughout Europe. In the 15th century, twenty-eight new ones were created, with another eighteen added between 1500 and 1625.[33] This pace continued until by the end of the 18th century there were approximately 143 universities in Europe and Eastern Europe, with the highest concentrations in the German Empire (34), Italian countries (26), France (25), and Spain (23) – this was close to a 500% increase over the number of universities toward the end of the Middle Ages.

Compare with the global spread of the printing press. Compare with the influence of the printing press on the Italian Renaissance (read about Demetrios Chalkokondyles).

Traditionally held to have begun in 1543, when were first printed the books De humani corporis fabrica (On the Workings of the Human Body) by Andreas Vesalius, which gave a new confidence to the role of dissection, observation, and mechanistic view of anatomy,[59] and also De Revolutionibus, by Nicolaus Copernicus. [wiki quote]

Meanwhile, medieval universities faced more and more problems, like [source]

Internal strife within the universities themselves, such as student brawling and absentee professors, acted to destabilize these institutions as well. Universities were also reluctant to give up older curricula, and the continued reliance on the works of Aristotle defied contemporary advancements in science and the arts.[36] This era was also affected by the rise of the nation-state. As universities increasingly came under state control, or formed under the auspices of the state, the faculty governance model (begun by the University of Paris) became more and more prominent. Although the older student-controlled universities still existed, they slowly started to move toward this structural organization. Control of universities still tended to be independent, although university leadership was increasingly appointed by the state.[37]

To finish with a quote from the same wiki source:

The epistemological tensions between scientists and universities were also heightened by the economic realities of research during this time, as individual scientists, associations and universities were vying for limited resources. There was also competition from the formation of new colleges funded by private benefactors and designed to provide free education to the public, or established by local governments to provide a knowledge hungry populace with an alternative to traditional universities.[53] Even when universities supported new scientific endeavors, and the university provided foundational training and authority for the research and conclusions, they could not compete with the resources available through private benefactors.[54]

So, just a symptom.

______________

UPDATE:  Robin Osborne’s article is a perfect illustration  of the confusion which reigns in academia. The opinions of the author, like the following one [boldfaced by me]

When I propose to a research council or similar body that I will investigate a set of research questions in relation to a particular set of data, the research council decides whether those are good questions to apply to that dataset, and in the period during which I am funded by that research council, I investigate those questions, so that at the end of the research I can produce my answers.

show more than enough that today’s university is medieval university reloaded.  How can anybody decide a priori which questions will turn out to be good, a posteriori?  Where is the independence of the researcher? How is it possible to think that a research council may have any other than a mediocre glimpse into the eventual value of a line of research, based on bureaucratic past evidence? And for a reason: because research is supposed to be an exploration, a creation of a new territory, it’s not done yet at the moment of grant application. (Well, that’s something everybody knows, but nevertheless we pretend it does not matter, isn’t it sick?)  Instead, conformity reigns.  Mike Taylor spends a post on this article, exposing it’s weakness  as concerns OA.

______________

UPDATE 2: Christopher Lee takes the view somewhat opposite to the one from this post, here:

In cultured cities, they formed clubs for the same purpose; at club meetings, particularly juicy letters might be read out in their entirety. Everything was informal (bureaucracy to-science ratio around zero), individual (each person spoke only for themselves, and made up their own mind), and direct (when Pierre wrote to Johan, or Nikolai to Karl, no one yelled “Stop! It has not yet been blessed by a Journal!”).

To use my nomenclature, it was a selected-papers network. And it worked brilliantly for hundreds of years, despite wars, plagues and severe network latency (ping times of 109 msec).

Even work we consider “modern” was conducted this way, almost to the twentieth century: for example, Darwin’s work on evolution by natural selection was “published” in 1858, by his friends arranging a reading of it at a meeting of the Linnean Society. From this point of view, it’s the current journal system that’s a historical anomaly, and a very recent one at that.

I am very curious about what Christopher Lee will tell us about solutions to  escape  wall-gardens and I wholeheartedly support the Selected Papers Net.

But in defense of my opinion that the main problem resides in the fact that actual academia is the medieval university reloaded, this  quote (taken out out context?) is an example of the survivorship bias. I think that the historical anomaly is not the dissemination of knowledge by using the most efficient technology, but sticking to old ways when revolutionary new possibilities appear. (In the past it was the journal and at that time scholars cried “Stop! it is published before being blessed by our authority!”, exactly alike scholars from today who cry against OA. Of course, we know almost nothing today about these medieval scholars which formed the majority at that time, proving again that history has a way to punish stupid choices.)

# Multiple peer-reviews, a story with a happy-end

I shall tell you the story of this article, from its inception to its publication. I hope it is interesting and funny. It is an old story, not like this one, but nevertheless it might serve to justify my opinion that open peer-review (anonymous or not, this doesn’t matter) is much better than the actual peer-review, in that by being open  (i.e. peer-reviews publicly visible and evolving through contributions by the community of peers), it discourages abusive behaviours which are now hidden under the secrecy, motivated by a multitude of reasons, like conflict of interests, protection of it’s own little group against stranger researchers, racism, and so on .

Here is the story.

In 2001, at EPFL  I had the chance to have on my desk two items: a recent article by Bernard Dacorogna and Chiara Tanteri concerning quasiconvex hulls of sets of matrices and the book A.W. Marshall, I. Olkin, Inequalities: Theory of Majorisation and it’s Applications, Mathematics in science and engineering, 143, Academic Press, (1979). The book was recommended to me by Tudor Ratiu, who was saying that it should be read as a book of conjectures in symplectic geometry.  (Without his suggestion, I would have never decided to read this excellent book.)

At the moment I was interested in variational quasiconvexity (I invented multiplicative quasiconvexity, or quasiconvexity with respect to a group), which is still a fascinating and open subject, one which could benefit (but it does not) from a fresh eye by geometers. On the other hand, geometers which are competent in analysis are a rare species. Bernard Dacorogna, a specialist in analysis with an outstanding and rather visionary good mathematical sense, was onto this subject from some time, for good reasons, see his article with J. Moser,  On a partial differential equation involving the Jacobian determinant, Annales de l’Institut Henri Poincaré. Analyse non linéaire  1990, vol. 7, no. 1, pp. 1-26, which is a perfect example of the mixture between differential geometry and analysis.

Therefore, by chance I could notice the formal similarity between one of Dacorogna’s results and a pair (Horn, Thompson) of theorems in linear algebra, expressed with the help of majorization relation. I quickly wrote the article “Majorization with applications to the calculus of variations“, where I show that by using majorization techniques, older than the quasiconvexity subject (therefore a priori available to the specialists in quasiconvexity), several results in analysis have almost trivial proofs, as well as giving several new results.

I submitted the article to many journals, without success. I don’t recall the whole list of journals, among them were Journal of Elasticity, Proceedings of the Royal Society of Edimburgh, Discrete and Continuous Dynamical Systems B.

The reports were basically along the same vein: there is nothing new in the paper, even if eventually I changed the name of the paper to “Four applications of majorization to convexity in the calculus of variations”.  Here is an excerpt from such a report:

“Usually, a referee report begins with a description of the goal of the paper. It is not easy here, since Buliga’s article does not have a clear target, as its title suggests. More or less, the text examines and exploits the relationships between symmetry and convexity through the so-called majorization of vectors in Rn , and also with  rank-one convexity. It also comes back to works of Ball, Freede and Thompson, Dacorogna & al., Le Dret, giving a few alternate proofs of old results.

This lack of unity is complemented by a lack of accuracy in the notations and the statements. […] All in all, the referee did not feel convinced by this paper. It does not contain a  striking statement that could attract the attention. Thus the mathematical interest does not balance the weak form of the article. I do not see a good argument in favor of the publication by DCDS-B.”

At some point I renounced to submit it.

After a while I made one more try and submit it to a journal which was not in the same class as the previous ones, (namely applied mathematics and calculus of variations). So I submitted the article to Linear Algebra and its Applications and it has been accepted. Here is the published version  Linear Algebra and its Applications 429, 2008, 1528-1545, and here is an excerpt from the first referee report (from LAA)

“This paper starts with an overview of majorization theory (Sections 1-4), with emphasis on Schur convexity and inequalities for eigenvalues and singular values. Then some new results are established, e.g. characterizations of rank one convexity of functions, and one considers applications in several areas as nonlinear elasticity and the calculus of variation. […] The paper is well motivated. It presents new proofs of known results and some new theorems showing how majorization theory plays a role in nonlinear elasticity and the calculus of variation, e.g. based on the the notion of rank one convexity.
A main result, given in Theorem 5.6, is a new characterization of  rank one convexity (a kind of elliptic condition) […]  This result involves Schur convexity.

Some modiﬁcations are needed to improve readability and make the  paper more self-contained. […] Provided that these changes are done this paper can be recommended for publication.”

_________________________

PS.  The article which, from my experience, took the most time from first submission to publication is this one:  first version submitted in 1997,  which was submitted as well to many journals and it  was eventually published in 2011, after receiving finally an attentive, unbiased peer-review  (the final version can be browsed here)The moral of the story is therefore: be optimistic, do what you like most in the best of ways and be patient.

PS2. See also the very interesting post by Mike Taylor “The only winning move is not to play“.

# Anonymous peer-review after 15 months

I reproduce further the message sent by  a journal, 15 months after the submission. The message contains comments made by anonymous referees.

Let me stress that:

• I trust the journal, otherwise why submitting to it?
• this is the result of the anonymous peer-review  after they sit on the paper for 15 months,
• I suppose that the extracts from the reports, provided to me by the managing editor, are the most significant ones, otherwise the message makes no sense,
• the message is reproduced as it is, with the exceptions of links, added by me, the numbering of the referees’ comments and very few comments of my own, [between brackets], where I really could not stop myself.
• I removed the names of the managing editor and journal, in order to present the comments in a more objective light.   UPDATE: in fact, there are no reasons to protect maybe the most  sloppy peer-review report obtained in the most ridiculous amount of time. The journal is Geometry and Topology. The referees were anonymous, so they could pretend they read the article (but see referee’s comments (3), (6) and (7) which are evidence that at least one of them did not bother to read it in FIFTEEN MONTHS). As for the reason of rejection, because what is written in the reports cannot be one, rationally, I can only speculate.

The achieved effect is to keep this paper out of publishing for a year and a half. This article was written in 2009 and it has been previously submitted to:

• Commentationes Mathematicae Universitatis Carolinae (july 2009), retired from CMUC  (april 2010), after no referee report in sight; the reply of the editor was: “I am sorry for the long time you had to wait, and I understand your decision. I informed already our referee (who appologizes as well, but points out that your paper is very difficult to read and check)”
• Groups, Geometry and Dynamics, (april 2010), received the following answer (august 2010): “I am sorry for such a late answer, but after consulting with referees and other editors, we arrived to the conclusion that your paper does not fit the scope of our journal.”
• Electronic journal of Combinatorics (january 2011), answered (january 2011):  “I have looked at your paper in the arXiv. It’s really outside the scope of E-JC. You need to send it to one of the journals mentioned in your reference list or some other geometric/algebraic journal.”
• Constructive Approximation (nov. 2011), received answer (nov. 2011):  “I had an editor quickly look over your manuscript. He suggested that the article is more appropriate for a journal that publishes papers in algebra and geometry. Here is the response we received from the editor: —————- The paper is interesting. It studies the relationship between algebraic and differential structure on manifolds with sub-Riemannian geometry, in particular, Carnot-Caratheodori metric. Such questions are natural in the framework of rigidity theory. I do not know why he submitted the paper to CA. It should be sent to a journal that publishes papers in algebra and geometry. It can be a general journal (like Journal of LMS) or a more specialized journal like “Geometry and Topology” or IJAC (“International Journal of Algebra and Computation”). —————-“
• Geometry and Topology (2 dec. 2011),answered (11 march 2013), see further.

The article just not fits   in a place.

_____________________________

Here is the message from the managing editor of Geometry and Topology:

“Dear Prof. Buliga,

I regret to inform you that your paper

Emergent algebras

has been rejected by G&T . I attach an extract from the referee’s report. Your paper was sent to two referees, and their conclusion was that the though the results are interesting he paper cannot be published in the current form. The referees’ reports are addressed to the editors, so I only give you at the end of this message some extracts from both reports. The editors would be willing to consider your paper again if it is appropriately rewritten.

On behalf of the editorial board I would like to thank you for giving us the opportunity to consider this paper for G&T.

Sincerely

Yasha Eliashberg , Managing Editor of Geometry & Topology
Selected comments from the referees:

(1) I find the paper a bit confusing. the comments give the impression that the theory encompasses manifolds (and sub-Riemannian manifolds), but, if I am not misled, the results only concern groups.  I find the quandle characterization of Carnot groups striking. but the paper needs rewriting.

(2) The second paragraph of the abstract should say “… are related to racks and quandles…” Quotes in TeX should be of the form “this phrase is in quotations.” Many people make that mistake — it is an annoying feature of TeX, but I find it off-putting when and author  does not fix this. The second item on page 2 the word should be: information line -14 page 2 “obtain” should be “obtained.”

(3) The paper starts Introduction, Outline, Motivation and I still don’t know what the author wants to achieve. I am not an expert here, but I still want some ideas. What, for example is a Carnot group?

[So, there are 3 sections of the article full of explanations of the ideas, but not enough. Moreover, Carnot groups are defined in Definition 4.6 in the article. Even without reading the article, as this referee,  one can still find what a Carnot group is, for example by using google, or a trip to the library]

(4) newtheorem environments default to italics. 3.1,3.2 etc should be set in roman font.

(5) After definition 3.3, example 4.1 should be given. Also, delta should be exemplified. Here there is something very interesting from the  point of view of quandles: delta is NOT necessarily an automorphism.  The reader needs examples to continue.

(6) On page 6 above Remark 3.4, I don’t see the definitions for the original circle operations.

[They are in Definition 3.3, exactly where the referee does not see them.]
I can’t think of a scenario in which )this( is a meaningful grouping. There are several grouping operations provided in TeX; please use one.
At (a), (b), and (c) I got lost in the notation.
… It took me some time to see that the advantage is the statement of  Prop.3.5  and the remarks that follow.  [Thank you!]

(7) I think that the point of the paper is the paragraph on page 10 above Def. 4.6. I would like to see some more exposition about this early.

[Section 2 “Motivation” is dedicated to this.]

8) What is $n$ in the definition 4.6? In 5.3, do X and Y have the same first operation? Why not an empty diamond or filled one for Y?

(9) My overall impression is that the author has a very nice big idea: geometry and algebraic structures emerge togther in a manifold situation. He is arguing that irqs and/or symmetric spaces give rise to tangent-like structures. But I would really like a careful  exposition with detailed examples written for a less selected  audience.”

_______________________

UPDATE 2: I submitted the article to another journal. I hope it is clear that what I am after is fair, rock-solid peer review, which I could learn from and which could improve the article. It is obvious that I think the emergent algebra idea is gorgeous, as the author of it I naturally support it, but not to the point of  not accepting critics. But they have to be real critics, with substance and then I welcome them and follow them. That is why I submitted the same file, the one available from arXiv; that is already version 3 and previous versions do not differ much. If I change it then I have to produce a new version, but the substance of the article is well enough (according to my powers) communicated, but not really understood by any of the referees until now. It can be improved, even enormously, and I shall do it eventually, but for the moment, this is really not worthy if the referees are put off by the use of ” or by “obtain -obtained” matters. Maybe I am wrong, surely I am wrong in this respect, but also my past experience tells me that it does not matter how well I present a new idea if the referees don’t really read the paper. This is not meaning I encourage sloppy articles, if you read it then you will see that the paper is densely and carefully written, maybe even too optimized, as the referee’s comment (6) shows. But hey, we are in the internet age, there is no reason anymore to present things as if they are designed to be read in front of a (bored) audience. We have google, we are multitasking, we use hypertext.

# What could be built on top of a World Digital Math Library?

The title is copy-pasted from the following question by Ingrid Daubechies, on mathforge.org [I added some links]:

Suppose most mathematical research papers were freely accessible online.

Suppose a well-organized platform existed where responsible users could write comments on any paper (linking to its doi, Arxiv number, or other electronic identifier from which it could be retrieved freely), or even “mark it up” (pointing to similar arguments elsewhere, catch and correct mistakes, e.g.), and where you could see others’ comments and mark-ups.

Would this be, or evolve into, a useful tool for mathematical research? What features would be necessary, useful, or to-be-avoided-at-all-costs?

This is not a rhetorical question: a committee of the National Research Council is looking into what could be built on top of a World Digital Math Library, to make it even more useful to the mathematical community than having all the materials available. This study is being funded by the Sloan Foundation.

Input from the mathematical community would be very useful.

________________

UPDATE:  David Roberts points to the fact that Daubechies asked the same question at mathoverflow before asking at mathforge. The answers are much more welcoming there, interesting read.

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Notice: “a World Digital Math Library”, not “the World Digital Math Library”. Concerning the involvement of the Sloan Foundation, that would be great, let me cite again the Conjecture 4 by Eric Van de Velde, proposed  in   MOOCs teach OA a lesson:

OA is not sufficiently disruptive. Hoping to minimize resistance to OA, OA advocates tend to underemphasize the disruptiveness of OA. Gold and Green OA leave the scholarly-communication system essentially intact. When presented in a minimalist frame, they are minor tweaks that provide open access, shift costs, and bend the cost curve. Such modest, even boring, goals do not capture the imagination of the most effective advocates for change, advocates who have the ears of and who are courted by academic leaders: venture capitalists. This is a constituency that seeks out projects that change the world.

There seems to be two camps in the discussion about comments for articles as a tool of mathematical communication:

• the cons: few, very vocal, are using the straw man argument that comments to articles are like comments in blog, therefore unreliable. It is my interpretation that in fact this is motivated by fear of authority loss. Maybe I am wrong, anyway their argument is blown away by one fact which I shall mention further.
• the pros: they are not disputing the utility of the tool, they would like to have more details instead, about what exactly will be comments for: a kind of online perpetual peer-review, will be them considered as original contributions, where do comments sit in the continuum between the original article and its peer review and, most important, how to motivate mathematicians to seriously participate.

I think the formulation of the question by Ingrid Daubechies is precise and very interesting. Accordingly, mathematicians from both camps could take some moments to think about it.

Is this the kind of disruptive idea which could make the people dream about, concerned about, and also, very important, which could be considered as world-changing? I certainly hope so.

Let me close with the funniest argument (in my opinion) against the idea that comments are bad, because they are like comments in blogs. You see, there is an elephant in the room. Who invented blogs? Why, a mathematician, John Baez with his This Week’s finds. And what exactly is the content of Baez’ first blog in the world? Well, dear naysayers, it is about comments by John Baez of mathematical (and other) scientific articles.

John Baez participates to the discussion initiated by Ingrid Daubechies with this:

I would like some way for me to be able to easily read lots of comments on people’s papers.  Right now to find these comments I either use Google or trackbacks on the arXiv.  But I think there could be something better.
To be honest, I mostly want to read my own comments on people’s papers, because I wrote a lot of them in This Week’s Finds, and nobody else writes nearly enough.  I don’t have much trouble finding my own comments: I use Google, and use keywords that single out This Week’s Finds.  But it’s harder finding comments when I don’t know who wrote them or where they are.

Congratulations John Baez, you are an example for many of us!