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Until recently, science was structured in "hard" vs. "soft" disciplines.

With a slight oversimplification, "hard" sciences were fields where the problems were formulated and solved within a mathematical language based mainly on (partial differential) equations. The archetypal"hard" science was physics and for any discipline to progress quantitatively it was supposed to emulate its example. In fact chemistry became "harder" as the use of the Schroedinger equations to describe chemical processes became possible.

Biology, recognizing the impossibility of reducing its matter to equations developed a defensive attitude of mistrust against theoretical explanations while economics had often chosen the opposite road: to sacrifice detailed quantitative confrontation with empirical data for the sake of closed tractable models.

The study of innovation, creativity and novelty emergence had chosen to ignore the "Newtonian paradigm" altogether taking sometimes even pride in the ineffable, irreducible, holistic character of its subject.

This was natural, as the mechanisms allowing the understanding of phenomena in those fields are most probably not expressible in the language of equations.

Fortunately it turns out that equations are not the only way to express understanding quantitatively. In fact, with the advent of computers one can express precisely and quantitatively almost any form of knowledge.

E.g. adaptive agents, can "learn" certain tasks by just inputting lists of "correct" and "incorrect" examples, without any explicit expression of the actual criteria of "correctness" (sometimes unknown even to the human "teacher").

This relaxation of the allowed scientific language and the focus on the emergence of collective objects with spatio-temporal (geometrical) characteristics renders the scientific discourse more congenial to the "daily" cognitive experience and to practical applications.

One can now formulate in a precise "hard" way any "naive" explanation by simulating (enacting) in the computer the postulated elements and interactions. One can then verify via "numerical experiments" whether these "postulates" lead indeed to effects similar to the ones observed in nature. The computer can deal simultaneously with a macroscopic number of agents and elementary interactions and therefore can bridge between "microscopic" elementary causes and "macroscopic" collective effects even when they are separated by many orders of magnitude.

The following steps are a first sketch of the main ideas:

Microscopic Representation

Represent the (continous) system in terms of (many) "microscopic" agents ("elementary degrees of freedom") which interact by simple rules.

Collective Macros

Identify sets of (strongly coupled) elementary degrees of freedom which act during the evolution of the system mostly as a single collective object (macro).

Effective Macro Dynamics

Deduce the emergence of laws governing effectively the evolution of the system at the Macros scale as a coarse (average) expression of the simple rules acting at the elementary level.

Emergence of Scale Hierarchies

Apply iteratively to the Macros systems at various scales the last two steps. This leads to a hierarchy of Macros of Macros (etc.) in which the emerging laws governing one level are the effective (coarse) expression of the laws at the finer level immediately below.

Universality

The general macroscopic properties of the coarsest scale depend on the fundamental microscopic scale only through the intermediary of all the levels in between (especially the one just finer than the coarsest). This usually means that relevant macroscopic properties are common to many microscopic systems. Sets of microscopic systems leading to the same macroscopic dynamics are called universality classes.

Irreducible complex kernels

One can show that there exists classes of (sub-)systems for which one cannot reexpress the fundamental microscopic dynamics in terms of effective interactions of appropriate macros. We call them Irreducibly complex (ref). Such (sub-)systems are in general non-universal and their properties are in many respect unique. All one can do is to become familiar with their properties but not to explain (understand) them as generic / plausible consequences of the functioning of their parts. If in the process of analyzing a system in terms of a macro hierarchy one meets such irreducible kernels, the best thing is to treat them as single objects and construct explanations taking them and their interactions as the starting point (i.e. as a given input).

The main message of the Multi-Agent Complexity approach is that domains, fields and subjects which until now seemed to allow a continuous infinity of possible variations of their behaviors, may be treated in terms of a limited number of discrete objects (macros) subjected to a discrete limited number of effective rules and capable to follow a rather limited number of alternative scenarios.

This greatly limits the options for the effective macroscopic dynamics and the effort to analyze, predict and handle it.

In turn, the Macros and their effective rules can be understood (if one whishes a finer level of knowledge) in terms of a limited set of interacting components.

The criticism of the above scheme can range between "trivial" to "far fetched" but it turned out to give non-trivial valid results in a surprisingly wide range of problems in theoretical physics (ref), chemistry (ref), computational physics (ref), image processing (ref), psychophysics (ref), spin glasses (ref), ultrametric systems (ref), economy (ref), psychology (ref) and creative thinking (ref).

Next: Multi-Agent Complexity is intrinsically Interdisciplinary
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