|
Below, find a few remarks made on this paper by the reviewers
of Complexity International, followed by my replies.
Reviewer 1:
In the section dedicated to "Structure", before the first formulae,
there is the idea that the mathematical description only allows for a
static view of the objects described. I would relativize that issue,
since mathematical descriptions can well include within their own
formulation a possible evolution of the model (see logics of action,
temporal logics, or some categorical treatments in theoretical
computer science).
Reply:
To indicate my acquaintance with such ideas, I should probably have made
a reference to some book containing an overview of the related branches
of mathematics — e.g. D.A.Pospelov, Situation-driven control:
Theory and practice (Moscow: Nauka, 1986). I am not inclined to relativizing the issue, since, up to now, any attempts of incorporating time (movement,
functioning, evolution) in mathematics were entirely
structural, as far as I can judge. Today, mathematical reasoning is
poorly suited to discuss dynamics, or development; the present trend towards ever more abstract formality indicates
that functional and developmental ideas can hardly receive an adequate
expression in the mathematics of the nearest future.
Additional considerations on the subject could be found in:
P.B.Ivanov, Computability in developing systems (1996).
There is yet another aspect, the common prejudice about the essence
of science. Traditionally, a scientist is supposed to
treat a very narrow and special subject, and any generalizations
are to be presented as if they had been made on the basis of
the bulk of such special investigations. But the true logic of
scientific research is exactly the opposite: any special research is
always regulated by some general considerations which determine
the choice of subject, the methods of research and the ways
of interpreting the results. There is no science without such a
conceptual background, and the attempts to disguise this important circumstance by a primitive inductive style are mere relics of a centuries-old
philosophy (F.Bacon etc.), slightly renewed by the logical positivism of
the XX century. I suppose that it's high time to abandon that
stylish primitivism in order to make scientific papers more logical, and indicating
the place of any special choice in a wider picture. In particular,
the arrangement of the results might better reflect the natural direction
of activity, from general ideas to their implementation.
Reviewer 1:
The following use of mathematical notation is rather awkward, and a
much more elegant presentation could be done using category theory for
instance (however I doubt it would really be necessary, when one looks
at what is achieved using this pseudomathematical model: mere
introduction of the notion of structural complexity as an entropy-like
function).
Reply:
Complexity International started as a methodological journal,
trying to synthesize the variety of applied research into an integral
view of complexity in general. My paper was an attempt to revive this
orientation, which has eventually become dissolved in the rush of
highly technical papers of the last volumes. Here, mathematics serves
as a mere illustration of general ideas, and I didn't
intend to obtain any formal results, which is stressed by the very
title of the paper. Simple notions are better suited for illustration,
so that I don't have to waste two thirds of the text explaining the
notation. Yes, the category theory is an amusing toy; but it
develops in the same conceptual frame as the rest of mathematics,
and brings no principal novelty in the discussion of fundamental problems.
I would stress once again that structural complexity is not a number, since
any numerical estimates of complexity belong to a different level, namely,
that of multiplicity. Structural complexity
can be represented by a hierarchy of numerical measures of
complexity, but it can never be reduced to any specific measure.
Rather, different structures might be used as the units of
structural complexity, just like numbers measure multiplicity.
Reviewer 1:
In the section on "System", there is a reference to Gödel, which
could be skipped. The idea that functional complexity is only revealed
dynamically and that a mathematical description is a priori static, is
not very closely related to the incompleteness theorems.
Reply:
I agree, that the relation between the incompleteness theorem and
the insufficiency of the structural approach of mathematics should
be additionally clarified. In this paper, I express my opinion without a due
substantiation, which is is far from the current style
of "scientific" reports. According to the present norms,
I should first have publish a paper on the Gödel theorem, and then
quote it in context of this discussion. Unfortunately,
there is logical circularity: such a paper on incompleteness would necessarily involve
the ideas expressed in the present paper, which should hence have been presented beforehand... A phrase might well be skipped, to please the reviewer;
still, still, I'd rather leave it as it stands, since the
paper will not be published anyway.
Reviewer 1:
I enjoyed the multiple foldings involved in the section on
"Hierarchy", it is an interesting idea of the whole paper.
Reply:
Thanks. This is a very important feature of hierarchies,
with numerous examples in the literature, albeit without a clear awareness.
Reviewer 1:
The conclusion is very speculative, and personnally I do not share
such dream visions. I would greatly recommend a rewriting of that
conclusion.
Reply:
Sorry, but I hate the style of concluding sections that just
list the "main results" of the paper, duplicating the abstract or/and
the introduction. For some papers, that could do; but only
for those in the traditional line, pretending to establishing
final truths. A piece of work that has not yet been (and, in fact, can never be) finished
should better conclude by indicating the ways of further development, or suggesting additional conceptual links to think over.
Reviewer 2:
English: a lot of mistakes (about 16 on the front page only)
Reply:
Since English has become the language of international communication
in science, there is a flavor of language chauvinism
in academic journals: native English-speakers are more likely to
pass the barrier, and the references to non-English sources are
discouraged; in any way, reviewers now have a quick excuse for rejecting a paper without going into any particulars.
Everybody knows that efficient communication does not require
perfect phrasing, or correct spelling: all the misunderstandings
can be fixed in the flow of communication. Those interested in the ideas would not waste time counting language lapses.
Reviewer 2:
A paradigm is discussed which defines complexity in terms of
"integrity", "structure" and "system". Part of the discussion is
mathematical, the rest being merely philosophical. Despite very
interesting ideas, its content is often inaccurate (for instance:
"Structure is more than just elements and links, it is a kind of
wholeness, a level in the hierarchy of integrity") and conclusions are
hazy ("Functional complexity leads to the numerous forms of Gödel's
theorem"). The math parts are a bit basic.
Reply:
Well, I have to admit it. The discussion is mainly methodological,
with minimum mathematics, just for illustration. It would be nice to
learn which particular ideas have attracted the reviewer's attention. Still,
I do not find any inaccurateness in the quoted sentence
on the essence of structure; in fact, it is much more accurate than
the usual mathematical definitions, reducing structure as such to arbitrary special models.
Reviewer 2:
My advise would be to read "Chaos and Information Theory: an heuristic
outline", Nicolis and Prigogine, World Scientific, 1990.
Reply:
I am well acquainted with the Prigogine's line (and I reference one of Prigogine's books in the paper). My approach is quite
different; though, of course, I appreciate the value of
Prigogine's ideas for the comprehension of the necessity of
incorporating development in science. However, I suppose that
his theory deals with only one of the possible kinds of development, and that it is insufficient
in other cases (especially, in social sciences). This is a topic for
a special discussion.
With all that, why should I discuss somebody else's views in my text instead of those of
my own? And why should my views merely expand somebody's
ideas, rather than follow my own way of thought?
Reviewer 3:
While the subject of making explicit various aspects of the
notion of complexity is an appealing one, I think that the paper lacks
precision in its use of terms, and fails to present a logical and
rigorous argument from well defined contentions to conclusions.
Reply:
The principal goal of my paper was to clarify the ideas related to
complexity, and for that purpose, I suggest a new way of definition,
relating any notions to their hierarchical context. The reviewer
has missed that point, because of the common prejudice that the only precision
possible is that of syllogistic deduction. However, neither
deduction is the only source of rigor, nor can it be rigorous enough, as my previous paper,
Computability in developing systems, clearly indicates. The standard
form of discourse imposed by "scientific" journals is nothing but a
tribute to an obsolete tradition.
Reviewer 3:
In a paper of this kind one would expect to find:
1. In the introduction, a clear statement of the research question
being tackled including how the research builds on the existing body
of research. I would expect to find reference to specific papers
(rather than whole volume citations) defining the point of departure
of the research, what has gone before and what new methods are to be
employed. There is a substantial literature concerning the definition
of complexity.
2. In the body, clear definitions of terms, clear descriptions of
analytical models and methods to be used to make the argument, and an
economy of description demonstrating a clearly worked out argument.
3. A clear conclusion summarising the contribution of the research
and remaining open questions.
Reply:
This is a good summary of bad style. The numerous articles like that pretend
that they really contribute into development of science, while
timidly hiding any valuable thought in the haze of references to
the predecessors. Certainly, the text should be as clear as possible.
However, following the above formal requirements would rather obfuscate any problem.
-
An overview of the previous work in the same field adds nothing to the
contents of the paper, while increasing its size and obscuring the author's
intentions. Such historical issues should rather be treated in a
special appendix, or even in a separate paper devoted specifically
to the history of science.
-
Problems that have not yet been studied to any considerable extent cannot have a clear preliminary formulation. A concise exposition of the principal line of research
would restrict the problem to a particular approach, which may prove
utterly inadequate in the end. A general indication of the scope
is quite enough for an introduction, since it is the whole body of the
paper that is to exactly specify the issues to consider. Scientific
research differs from engineering in that the latter starts with a (more or less comprehensive) list of features to implement, while science is bound to
ramble in the dark to discover phenomena yet unknown.
-
"Precise" definitions are only possible within a very narrow portion of research,
where nothing really new is expected to come, beyond a rearrangement of
the already available. Activities like that may be of some use for certain pragmatic purposes, but they have nothing to do with science.
Likewise, the methods to employ will normally crystallize in the course of their
employment, and not before real research. To demonstrate a clearly worked
and economical argument, one needs to entirely solve the problem, which is impossible in any serious study. Such "sharpened" descriptions
appear much later, as simplified accounts, in the educational context.
-
A summary of the author's contribution in the conclusion would mean that a final solution is already at hand, which is almost never the case.
The only honest kind of summary is to remind what the author
did (but never have done) in the body of text; still, isn’t it what an abstract is for? The author can never enumerate the remaining
open questions, just because there is an infinity of such questions, including
those considered in the text. Of course, the author is free to speak of his personal interests and priorities; the reader may however be interested in anything else.
Reviewer 3:
Instead we find many undefined terms which have precise meaning only
for the author, a set theoretical model that is introduced and then
largely abandoned, and a rambling development which includes a number
of irrelevant metaphysical speculations.
Reply:
The reviewer did not pay attention to the specific type of definition employed in
this work: the categories mutually define each other through being used in
the same context, in different positions. This method of definition
is no less precise than the traditional reduction to something previously introduced (and which always needs to be somehow defined in its turn).
An illustration of some particular viewpoint (say, a set theoretical model of structure) may happen to be much less useful to illustrate a different idea; one does not need to stick to a single picture throughout the whole. "Metaphysical speculations"
(methodological research) are absolutely necessary to avoid blind technicality,
purposeless manipulation with empty symbols and arbitrary terminology.
Reviewer 3:
The paper demonstrates a lack of understanding of the incremental
nature of scientific investigations and the degree of precision required
for publication in a scientific journal.
Reply:
The reviewer demonstrates a lack of understanding of the impossibility of
incremental evolution in science, and the inevitability of scientific
revolutions. He confuses science with engineering, or mere craftsmanship,
denying any real creativity.
|
