Review 2 Response
Thank you for the second round of review of my paper Double Conformal Mapping: A Finite Mathematics to Model an Infinite World with the introduction of a third anonymous reviewer (reviewer “#4”).
It seems we have one reviewer still in favor of publishing the paper as is, and now two reviewers who oppose publication without substantial revision. Indeed the new third reviewer (reviewer “#4”) demands that the paper not only be substantially revised, he requires “beyond a major revision which can be compared to its original”. In other words this reviewer requires that the Biological Theory of Mathematics, and all its attendant evidentiary support, be dropped entirely, and the paper be rewritten from scratch on a topic of the reviewer’s choosing. Is it not the prerogative of the author to choose the subject matter of his own paper? The Biological Theory of mathematics is the central core, the prime thesis of the present paper! The introduction begins with that theme, the conclusion ends with that theme, and the entire paper is written in support of the Biological Theory of mathematics. That is what this paper is about! And that is what makes this paper so significant. If this paper were revised to meet with this reviewer’s approval I would no longer wish to be its author!
If the review process were a democracy then the paper is surely sunk, the tally against publication is now two to one. But if science were merely a democracy then really new and original ideas that challenge the established orthodoxy would never see the light of day.
Both dissenting reviewers object vehemently to discussion of the Biological Theory of Mathematics as if that discussion were not appropriate in a mathematical journal, and yet neither one of them explains why they oppose it, they merely demand that it be removed from the paper without discussion.
If the Biological Theory of Mathematics is so objectionable then why don’t these two dissenting reviewers explain 1: Why the Biological Theory of Mathematics is so objectionable that it cannot be discussed freely in a mathematical journal, and 2: How they can possibly support the alternative Platonic theory of mathematics over the arguments of the present paper that that theory is un-falsifiable in principle, and thus not a scientific hypothesis at all?
The deafening silence of these two reviewers on this central issue to the present paper surely reveals that they are themselves Platonists at heart, that they take the Platonic theory as an initial assumption that is not to be questioned, and thus they object to any paper that challenges the indefensible dogma that “everybody knows” to be the “established truth” about the origins of mathematics.
The Biological Theory of mathematics is profoundly revolutionary because it transforms mathematics from a mystical entity whose ontology is totally obscure, to a scientific entity with real existence in the physical world known to science. I am sorry to have to be the one to point it out, but this is a very significant advance in our understanding of mathematics.
Reviewer #4 (the new third reviewer) reveals his deeper personal prejudices against the paper by admitting that the paper sets off his “crackpot alarm” due to the “nonstandard affiliation of the author, the heavy self-referencing; the metamathematical drive; the Use of Capitals in weird places; the clumsy home-made drawings…” etc.
This comment sets off my “academic
When I first began submitting to peer reviewed journals a couple of decades ago, I thought that the academic world would be open and welcoming to fresh new ideas from unaffiliated outsiders. How naïve I was then to contemporary academic reality! I now realize that my “nonstandard affiliation” and my obstinate insistence on expressing my ideas clearly and simply without obsfucatory mathematical gobbledegook, are like a red flag to reviewers as a sure sign of an academic outsider without the proper credentials to be worthy of their exclusionary publications. This however is the first time I have ever seen that unspoken prejudice expressed openly in a review. I have long since given up on submitting to peer reviewed journals for the futile exercise that it has become. The only reason I submitted this paper to the AACA was because David Hestenes himself invited me to speak at ICCA10, and that invitation automatically included an invitation to submit a paper to the AACA on the proceedings of the conference.
There has been an unfortunate trend in the peer review process, due to the ever increasing pressure to publish for the purpose of career advancement, for the author to be treated as a supplicant, humbly begging for favor from a panel of skeptical judges, who are afforded the privilege of anonymity, thereby evading direct accountability for their judgements. This is hardly a peer relationship! The problem is exacerbated by the fact that editors are often very busy, and therefore they tend to defer their judgement to the reviewers, thereby elevating their role from that of "prosecution" representing one side of the case, to that of a panel of anonymous judges, deciding the issue outright.
In this case the editor even chose to completely ignore the positive review of reviewer #1 and instructed the author instead to focus on the pedantic quibbling of reviewer #2, and in the second round of review apparently allowed the new third reviewer (reviewer #4) to read the first round of review, (is that really impartial?) which prompted the new reviewer to “pile on” with the academic indignation of reviewer #2 at the insolence of an author who has the temerity to speak out in protest against an unfair and ignore-ant (of the central issue of the paper!) review.
The progressive degeneration of the peer review process to a committee decision by a panel of anonymous judges poses a particular obstacle for paradigmatic proposals like the present one, because the panel is necessarily composed principally of reviewers whose whole career has been committed to the older paradigm. So if the decision is made by majority vote, the committee decision almost always rules against the paradigmatic hypothesis.
I am not a career
scientist, I don’t need this publication for career advancement, I
since resigned myself to taking my kudos posthumously. I submitted this
as a favor to David Hestenes in case he wanted to refer his students or
colleagues to this interesting new variation on his own ground-breaking
mapping in an official publication instead of just on my informal web
where I now publish all my new ideas without censorship for academic
officialdom to ignore. Some reviewers view the review process as if
a class exercise where adherence to proper form and protocol is more
than actual content. Life is not a rehearsal. This paper is for real. It
interesting new idea, clearly stated and ably supported by arguments and
evidence. The fact that the dissenting reviewers heavily emphasize every
variation from conventional protocol while not only totally ignoring the
substantial content and novel concepts of the paper, but even demanding
that content be removed entirely
without question or appeal,
that these reviewers believe the review process is more like a class
than an exchange of ideas among co-equal peers.
This review is not a test of the validity of this paper and its significant contribution to mathematics. That much is already self-evident to anyone with the mathematical insight to recognize it. This review is a test of the relevance of the whole peer review process to the advancement of mathematical thought. If these reviewers are right, that publication in a peer reviewed journal is more a matter of proper form and protocol than of free expression of interesting new mathematical ideas in the author’s own words, then I would have no desire to have my paper published in the AACA under those conditions.
I refer back to the overlooked review by reviewer #1, evidently a man of exceptional insight and historical perspective, who wrote:
This paper is well written, highly original and interesting. It is also controversial at many levels. But that is to be expected, because the central thesis is so provocative, and supporting evidence is controversial. It would be unproductive to quibble about any particular point. Therefore, it should be published without change and let readers decide.
There speaks a man who understands what the review process should be all about.