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To reviewer C
We respect Reviewer C’s thesis, but we do wish to point out that the view of Complexity as a new paradigm is shared by a large part of the scientific community. Complexity clearly fulfills one of the basic premises of a paradigm in the sense of Kuhn by constituting a new way to pose and solve a set of problems in a certain scientific area. It represents a radical shift of perspective with respect to previously prevailing ideas by placing emphasis on probabilistic views, predictability, information processing, evolution, or adaptation.
Kuhn adds another, stronger condition that according to him a paradigm must fulfill, namely, the ‘incommunicability” of the knowledge acquired according to different scientific paradigms. Complexity is at variance with this strong statement. At no point does it claim that Newton’s laws and Mechanics in general would be false. As an example the concept of trajectory is not considered to be technically incorrect but, rather, as being no longer operationally significant in many situations of interest.
Now Kuhn’s second criterion is considered by many to be overly strong, as it overlooks the possibility of a dialogue in the evolution of science. We share this view and wish also to point out that our use of the term “paradigm” is compatible with the ontological origin of this concept as laid down by Plato.
In conclusion we believe that it is fair to admit that the concept of paradigm may be used legitimately in the sense advocated in our article, considering the numerous discussions found in the literature on the epistemological subtleties related to this type of issues. Since this response to Reviewer C is an integral part of the material accompanying our article, and given the fact that our view is far from being an isolated one, we wish to maintain the original formulation of the opening sentence of the article.
Answer from reviewer C:
The authors have nicely illustrated their point of view with some clear arguments. Nonetheless, I remain hesitant on the fact that we are really facing a paradigm shift. The authors correctly mention a number of elements that characterize a paradigm in the sense of Kuhn but they skate over the fact that, according to Kuhn, a paradigm shift happens to account for an empirical anomaly. Since I am not able to see an empirical anomaly behind the development of Complexity, I am more keen to consider it as a normal (in Kuhn's sense) development of classical mechanics.
I fully agree with the authors that this discussion will remain associated with the article: the interested reader will have the chance to see the arguments that we have raised and will be able to develop his/her personal opinion on this issue.
A final remark for the editor: For clarity, this page should be rearranged in chronological order.
To reviewers B and C:
The new version of our Scholarpedia article on "Complex Systems" is available for evaluation. The revision carried out addresses reviewers' comments referring to technical issues and to clarifications of some key concepts. We did not address, in the name of academic freedom, issues reflecting personal preferences or related to phrasing and style. Specifically:
Concerning Reviewer B's comments
-We clarified what constraints mean.
-We specified that uniqueness and stability at the probabilistic level refer to the invariant probability densities.
-We clarified the status of direct simulation with respect to the integration of a set of evolution equations.
Answer from reviewer B:
Yes, I accept the reference to academic freedom. Styles are really different.
Concerning Reviewer C's comments
-We rephrased the sentence on emergent properties.
-We corrected the typos.
Answer from reviewer C:
I cannot approve the current version of the article. The authors have not reacted in a satisfactory way to my first remark concerning the opening sentence of the article. This remark of mine does not address neither personal preferences of the authors nor matters of style. It rather concerns a technical issue: the concept of scientific paradigm and the implied concept of paradigm shift have a precise meaning in the fields of philosophy and history of science and I maintain that these concepts are used in the current version of the article in a way that is not correct. I cannot accept the invocation to academic freedom on this issue.
The general goal of this initial review is to make the text somewhat sharper, better defined. There are many ways to write about complex systems, so the sections used by the authors are accepted.
- First paragraph: Complexity is not restricted to science. The book Art and Complexity by J. Casti and A. Karlqvist may be cited.
- Second paragraph: I think the statement is not really true. It says (in less technical terms), that we can find less complex phenomena at microscopic and macroscopic scale, than at mesoscopic level. The statement should be justified, in any case.
To 'Phenomenology of Complexity
- "A system perceived as complex" : it gives the feeling of subjectivity. If the authors wants to suggest that the borderline between simple and complex system is not clearly defined, they should tell explicitly.
- It is not fortunate to use the expression "to choose". It gives the feeling that a physical system bring a conscious decision.
- after "population level": metabolic networks and food-web networks are extensively studied examples.
- To the "intertwining" paragraph: together with earthquake eruptions and stock market crashes, the onset of epileptic seizures should also be mentioned.
-"Nonlinear system under constraint": It should be clarified what constraints mean! Maybe it would be more precise to state, that theory of (linear and nonlinear) dynamical systems is a mathematical theory, while three school (theory of dissipative structures, synergetics and catastrophe theory) wanted to grasp many natural and social phenomena.
- instead of "evolutionary landscape" the "basin of attractor" is more precise.
- the master equation and Fokker-Planck equation: guarantee the uniqueness and stability of ++ stationary distribution and density ++.
-Predicting complex systems: The book Extreme Events in Nature and Society edited by S. Albeverio, V. Jentsch H. Kantz may be mentioned.
Simulating complex systems.
Probably a remark about the relationship of equation-based and agent-based models should be made. Than to mention deterministic and stochastic models. Simulation of equation-base deterministic models is equal to integrate (generally numerically) the equations. Stochastic simulation generates different "realization" of stochastic processes.
Evolutionary disciplines obviously emerged from biology now used in other disciplines (ev. computation, economy, psychology, linguistics, epistemology etc.)
The article covers in a nice way some fundamental issues that should be definitely addressed within Scholarpedia. I have few minor comments.
I think that the introduction should be rephrased. First of all, I think that the article should start by giving an explicit definition of a complex system. Moreover, I do not agree with the statement that is currently opening the article: "Complexity is emerging as a post-Newtonian paradigm". I do not think that complexity can be called a new paradigm since complex behaviors perfectly fit within the laws of classical mechanics. The theory of complexity has the invaluable merit of having "discovered" that systems described in classical terms may produce behaviors that were previously either unknown and unexpected or ascribed to disturbances, missing information, etc. In other words, complexity theory has shown that complexity is an intrinsic characteristic of a class of systems of classical mechanics. In this sense, complexity theory has definitely to be seen as a development of the Newtonian paradigm rather than as an alternative paradigm.
At the beginning of the section "Foundations of Complexity research", the concept of "emergent property" is unclear. In particular, when the system is described in terms of "collective variables" (that is, when the system is looked at as a whole and not as a collection of interacting parts) it does not make sense to speak of "emergent properties". The sentence should be rephrased.
Three lines before the end of the section "Foundations of Complexity research", a typo should be fixed: "principal quantities if interest" should read "principal quantities _of_ interest".
My comments on this nice article are as follows:
1.) Name and origin of this field of science: "Complexity" or "Synergetics" ? What is described in this article, especially in its sections on complexity, phenomenological complexity, foundations of complexity research, coincides precisely with the goal and early achievements of a field initiated as "Synergetics" in 1971  and worked out in 1977  and 1987 . This interdisciplinary field is documented in the Springer Series on Synergetics, with its more than 90 volumes since 1977, including topics such as physics, chemistry, biology, sociology, brain dynamics, etc.
More specifically, my comments are as follows:
2.) In their definition of complexity the authors write: "complexity is on the countrary rooted in the fundamental laws of physics". This is surely correct if this field is defined as referring to physics, chemistry and biology. But what about other fields, such as economy or sociology (fields covered by Synergetics)? According to the authors "the uniqueness of complex systems is that they have to do with a class of phenomena of fundamental importance in which the system and the observer may evolve on comparable time and space scales". But what about structure formation in astro-physics or molecular physics?
3.) The section on "characterization of complex systems" can become still more valuable if it will be worked out in more detail.
4.) References: H. Haken "Synergetics", Springer, Berlin, 1977. The complete title should be given, namely "Synergetics, Nonequilibrium Phase-Transitions and Self-Organization in Physics, Chemistry and Biology".
 H. Haken., R. Graham: "Synergetik - Die Lehre vom Zusammenwirken", Umschau 6, 191 (1971)
 H. Haken: "Synergetics. Nonequilibrium Phase-Transitions and Self-Organization in Physics, Chemistry and Biology", Springer, Berlin (1977)
 H. Haken: "Advanced Synergetics. Instability Hierarchies of Self-Organizing Systems and Devices", Springer, Berlin (1983)
 Springer Series in Synergetics: ca. 90 volumes since 1977. Series ed.: H. Haken
Even though the content of the article overlaps with the achievements in the field of synergetics, the article's title still should be "complex systems", as it talks not about a field, but about a type of systems (which could be studied by many methods from many disciplines). Thus, I will keep the present title unchanged.
- Eugene M. Izhikevich