Review 2 Response

Dear Editor,

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

This comment sets off my *“ academic
elitist”* alarm!

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
have long
since resigned myself to taking my kudos posthumously. I submitted this
paper
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
conformal
mapping in an official publication instead of just on my informal web
site,
where I now publish all my new ideas without censorship for academic
officialdom to ignore. Some reviewers view the review process as if
correcting
a class exercise where adherence to proper form and protocol is more
important
than actual content. Life is not a rehearsal. This paper is for real. It
is an
interesting new idea, clearly stated and ably supported by arguments and
evidence. The fact that the dissenting reviewers heavily emphasize every
minute
variation from conventional protocol while not only totally ignoring the
substantial content and novel concepts of the paper, but even demanding
that
that content be *removed entirely*
*without question or appeal*,
indicates
that these reviewers believe the review process is more like a class
exercise
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.