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To exemplify the formal equivalence which systems experience upon Multi-Agent formalization let us recount the story of the introduction of agriculture in Europe. Radiocarbon dating of artifacts associated with farming life shows that farming spread from Anatolia (now Turkey) to northern Europe in less than 2000 years (from 8 to 6 thousands years ago). This was termed as the "Neolithic Revolution" and it was associated among other things with the spread of the proto-indo-european language in Europe.

Figure 2: The points represent the archeological locations where farming artifacts were found. The colors represent the dating of those sites. One sees that the earliest points are situated in the Middle East while the later points are moving progressively to larger distances (one can show that the average distance increases linearly in time).http://marijuana.newscientist.com/ns/970705/features.html New Scientist 5 Jul 1997, Ancestral Echoes;  see also How was agriculture disseminated? The case of Europe © Paul Gepts 1999 PLS103: Readings - Lecture 13 http://agronomy.ucdavis.edu/gepts/pb143/lec13/pb143l13.htm

Among the theories proposed by the various groups in order to explain the spread of the Neolithic Revolution throughout Europe were:

• learning agriculture from neighbors (and transmitting it to other neighbors),
• sons/ daughters establishing farms next to parents farms,

In order to differentiate between the competing theories one has to analyze the macroscopic archeological (genetic, linguistic) data and compare with the results of the various postulated individual scale mechanisms:

The main feature which is however established is that the data are incompatible with a simple diffusion mechanism. Indeed, simple diffusion would imply an expansion of the farming territory which depends of the square root of time and a fuzzy boundary separating the farming territory from the unsowed territory. In reality the speed of expansion was constant in time and it advanced along relatively sharp (though irregular) boundaries.

This kind of behavior will be traced repeatedly in our examples to the discrete, auto-catalytic behavior of the microscopic dynamics.

As opposed to molecules diffusion, where the effect is dominated by the behavior of the bulk of the population (and therefore it lends itself to a local averaging treatment), here the pioneering, fore-running singular individuals (Eneas, the Asians which passed the Bering straits into America few thousands of years ago to become the ancestors of the American Indians, Columbus, Little Johnny Appleseed etc.), are the ones which impose the speed and the aspect of the system evolution.

More precisely once the individuals arrive in a "virgin" territory, they multiply fast to the level of saturating the new territory. So the colonization does not need to wait for the immigration of a large mass of colonizers from outside.

This crucial role of the individual elements and events requires therefore the use of the multi-agent modeling approach.

When expressed microscopically, the problem "reduces" formally to one very similar to the eq. (2.1) if one denotes by

n the carrier of the new language / technology (agriculture) and by

U the carrier of the old language / technology (hunting-gathering)

The postulated adoption of the new language and/or technology will be symbolically denoted by:

n+ U ---> n+ n + .autocatalysis equation 3

Our point is not  that the actual macroscopic dynamics in the two systems autocatalysis equation 1 and 3  are identical. The point is that the same formal elementary operations while leading to specific complex consequences are expressible and can be processed within a common universal and very elastic multi-agent autocatalytic formalism.

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