Dear Professor Eckhard Hitzer,

Thank you for your final rejection of my paper Double Conformal Mapping: A Finite Mathematics to Model an Infinite World.

This final outcome was perfectly predictable after even the first round of review when in the face of one glowingly positive review and one pedantic negative review, the editor chose to totally ignore the glowingly positive reviewer who recommended publication as is, and focused instead entirely on the negative reviewer who demanded not only a laundry list of quibbles over trivial technicalities, but also demanded that the core message of the paper be eviscerated and the paper be revised to a message not of the author’s own choosing. It was not a matter of "making use of the detailed suggestions of the reviewers in order to improve your paper" as the editor suggests. I would have been happy to attend to the details if that were all that was required. But I was not willing to eviscerate my paper of its core message and it was clear from the outset that the dissenting reviewers would never recommend publication with its core message intact.

The most outrageous aspect of this byzantine review process is that there is no accountability for the reviewers to defend even clearly absurd and indefensible objections. The only explanation these reviewers offered for demanding that the Biological Theory of Mathematics be removed entirely from the paper was that the Biological Theory of Mathematics does not exist! And the editor backs up this unreasonable demand because reviewers are always right, authors are not allowed to complain. But the existence of the Biological Theory of Mathematics is not something that has to be proven, merely stating the theory brings it into existence! The real objection of these two reviewers is that they do not subscribe to the Biological Theory of Mathematics, but they evidently cannot articulate their objections and thus they demand that the topic be banned altogether as a condition of publication. This is what is wrong with the peer review system! There is no allowance for open and reasoned debate. The reviewers' judgment is final, there is no appeal to reason!

I understand what a serious violation of academic decorum it is to complain about a review. My complaint not only guarantees certain rejection, but I will surely be blackballed from any further publication attempts. If the review process had any merit and decency, it should be about the ideas, not the person promulgating them. I apologize for my open rudeness, sometimes it is the only way to get attention. But if it is a violation of academic protocol to complain about an unreasonable review, then academic protocol is itself an affront to reason! It was the reviewers who began the rudeness by demanding that the paper be fundamentally rewritten with its primary message removed, without offering any reasonable explanation for its removal. And the editor compounded this insult to reason by ignoring reasonable objections. If the review process is not about reasonable discussion of interesting new ideas, then it has outgrown its relevance and become a useless vestige of its original purpose.

The real reason the dissenting reviewers demand removal of the Biological Theory of Mathematics is because it is a paradigmatic hypothesis, one that challenges the foundational assumptions that we all learned in school. This is not the first paradigmatic idea I have proposed. In 1999 I proposed that everything we perceive around us is an image inside our brain. Although it was a paradigmatic departure from the consensus view, it was a simple idea, clearly stated, and ably supported by argument and evidence. And it was met with the same howls of protest from reviewers as seen in the present review. In the first round there was one visionary reviewer who recognized the significance of the idea and recommended publication as is. The second reviewer objected vehemently and suggested the paper be substantially revised and submitted elsewhere. In response to my reasoned rebuttals the editor  simply recruited more reviewers to a total of three, and in the third round added two more for a total of five reviewers, each with their own laundry list of material to be added that expanded the paper to three times its original length, and in this round the editor chimed in personally and complained that I had not proven my case that if mind is the operation of the physical brain, then it is possible to infer the properties of the brain from the observed properties of the mind. I explained to the editor that this is a paradigmatic hypothesis, at least equally valid to the alternative consensus hypothesis which itself has never been proven, that you cannot see your brain from inside your mind. To his eternal credit the editor, Professor Stevan Harnad, was persuaded by reasoned argument not that the theory was right, but that it was at least as valid as the alternative, and thus deserving of release to the wider public to let people decide for themselves. The paper was finally published after four and a half years of review and five reviewers!

I learned from that review that when reviewers object to a paradigmatic hypothesis, they first insist that the idea is invalid for discussion because "everybody knows" it to be false, then recommend a laundry list of specific points that "at a minimum" must be addressed, because it is easy in the next round of review to simply declare that the revision was insufficient and the paper is quietly rejected. It is this kind of quiet rejection that provokes rudeness from the frustrated author.

The idea that the world of our experience is a three-dimensional "picture" inside our brain, is not entirely unrelated to the Biological Theory of Mathematics, or to the Conformal Mapping of Geometric Algebra. It demonstrates that our brain is first and foremost a three-dimensional imaging mechanism, capable of generating three-dimensional real-time moving colored images as rich and complex as the world you see around you now. And that in turn challenges contemporary neuroscience which has so far failed to find images in the brain. The fact that Geometric Algebra offers a particularly good model for wave-like phenomena, and the fact that algebra is geometric in nature, and the fact that synchronous oscillations abound in the brain, are all consistent with a wave-based imaging mechanism in the brain that sweeps out the image of our experience, and that incidentally offers an ontological explanation for the existence of mathematics, music, rhythm, and ornamental art, as artifacts of the computational mechanism of our brain.

But those are big ideas, too big to fit into a single paper, and apparently impossible to squeeze through the screen of the baroque "peer-review" process, whose mesh size is apparently limited by the smallest-minded reviewer on the review panel. It makes one wonder what ever happened to Reviewer #1 who said:

"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 changes and let the readers decide."

Was this review ignored because the reviewer did not provide the laundry-list of trivial criticisms that is customary in the review process? Who is this man? Is he an idiot to be ignored? Or is he perhaps the only one who understands what the review process is supposed to be about.

Steven Lehar

First Review
Author's Response
Second Review
Author's Response
Final Rejection