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In the preceding discussion we argued that complex macroscopic systems can be described, explained and predicted by the Multi-Agent Models of the interactions between their "elementary atoms".

">How does one decide what these atoms should be?

If they are chosen too close to the macroscopic level, the strength of the resulting scientific explanation is diminished: explaining that a car works because it has wheels and engine is not very illuminating about the heart of the matter: where does it take the energy and how does it transform it into controlled mechanical motion?

If the atoms of explanation are sent to too fine scales, one gets bogged into irrelevant details: e.g. if one starts explaining the quantum mechanical details of the oxidation of hydrocarbon molecules (fuel burning) one may never get to the point of the car example above.

Beyond the practicalities of choosing the optimal level of Multi-Agent, one can discern certain features which are of principle importance.

They set the natural limits of reductionism, of explanation, of understanding, of science in general and of sciences among themselves.

It is instructive to consider the following example in which the reduction is guaranteed by construction, yet completely ineffective.

Consider a program running on a PC. In principle one can reduce the knowledge of the program to the knowledge of the currents running through the chips of the computer. Yet such a knowledge is not only difficult to achieve, validate and store, but it is also quite irrelevant for what we call "understanding".

The right level of detail for understanding in this case is the flow chart of the algorithm implemented by the program (and in any case a level coarser than the "assembler" instructions of the machine).

In the same way, the problem of reducing mental activity to neuron firings is not so much related to the issue of whether one needs in addition to the physical laws assumptions of a "soul" which is governed by additional, transcendental laws. Rather, the question is whether the generic (non-fine-tuned) dynamics of a set of neurons can explain the cognitive functions. In fact, after millions of years of intensive selection by survival pressures, it is reasonable to assume that the system of neurons is highly non-generic, depending of all kinds of improbable accidents and therefore a totally reductionist approach to its understanding (relying on the generic properties of similar systems) might be quite ineffective.

However, let us not forget that if a system is numerically unstable during its Multi-Agent Simulation this might reflect also in a functional instability of the natural system too. Therefore, the failure of the "naive" Multi-Agent Simulation method, may signal problems with the formulation of the problem or a certain irrelevance to the natural reality.

This is not so when the fine tuning is fixed once for ever by the fundamental laws. For instance the role of water in the metabolism of all living systems depends very finely on the value of the energy excitation of some specific electronic quantum level. In fact the small change in this energy level induced e.g. by using "heavy" rather then normal water is enough to completely disable its proper metabolic function.

In this case, the numerical instability in computing the phenomenon does not lead to functional instability of the natural system, since the water molecule properties are universal and fixed once for ever. Even if a quantum-mechanical computation could prove that those numbers just come out the right way for sustaining the metabolism of living entities, this would not constitute more of an explanation than computing the motion of the balls in a lottery to explain why the numbers of your mother in law came up twice. 

These examples indicate the very important characteristic of the complex irreducible systems:

the emergence a non-generic systems, disturbing the applicability of the Multi-Agent Simulation procedure is associated with the borders between sciences. Once concluding that certain biological properties (as above) are not explainable by generic chemical and physical properties of their parts, it is natural to consider those biological properties as a datum and try to concentrate the understanding efforts to their consequences rather than their "explanation" in terms of their parts.

Indeed, irreducible complexity is related with the fact that every detail of the system influences all the other details across the system: there is no possibility to divide the system into autonomous sub-systems responsible for well defined "sub-tasks" [Simon, Rosen].

The reduction of biology to chemistry and physics is not invalidated here by the intervention of new, animistic forces, but by the mere irrelevance of our reductionist generic reflexes to a non-generic fine-tuned situation.

The situation is similar with being given the map of a complicated labyrinth: one can have the knowledge of each wall and alley (neuron, synapse), still it would take highly non-trivial effort to find the way out.

Even finding (after enormous effort) a way out of the labyrinth would not mean "understanding" the system: any small addition or demolition of a small wall would expose the illusory, unstable nature of this knowledge by generating a totally new situation which would have to be solved from scratch.

By its very dismissal in explaining this kind of irreducible-complex systems, the Multi-Agent Simulation is offering science one of its most precious gifts. It allows the retracing of the conceptual frontiers between the various scientific disciplines. The boundary is to be placed  at the level where there is a non-generic irreducible object which becomes the building block for an entire new range of collective phenomena.

More specifically, Multi-Agent Complexity is teaching us when a reductionist approach is worth launching and where are the limits beyond which it cannot be pushed: where the generic Multi-Agent Simulation dynamics has to be applied and where one has to accept as elementary objects specific irreducibly complex structures with "fine-tuned" fortuitous properties.

While such irreducible objects might have fortuitous characteristics, lack generality and present non-generic properties, they might be very important if the same set of core-objects / molecules /organelles appears recurrently in biological, neurological or cognitive systems in nature.

Recognizing the "irreducibly complex" parts of a complex system (rather than trying vainly to solve them by Multi-Agent Modeling means) might be a very important aspect both conceptually and computationally.

In such situations, rather than trying to understand the irreducibly complex objects and properties on general grounds (as collections of their parts), one may have to recognize the unity and uniqueness of these macros and resign oneself in just making an as intimate as possible acquaintance with their features.

One may still try to treat them by the implicit elimination method [Solomon95,Baeker97] where the complex objects are presenting, isolating and eliminating themselves by the very fact that they are projected out by the dynamics as the computationally slow-to-converge modes.

One could look at the necessity to give up the extreme reductionism (going with the reduction below the first encountered non-generic object) as "a pity". Yet one has to understand the emergence of these nontrivial thresholds as the very salt which gives "taste" to the world as a WONDERfull place where unexpected things which weren't "put by hand from the beginning" can emerge. Moreover one should be reassured that the fundamental "in principle" reduction of macroscopic realty to the fundamental microscopic laws of the material reality is not endangered (or at least not more endangered than it started with).

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