19052 - The Omadologia

N. Lygeros
Translated from the Greek by Athena Kehagias

Leibniz’s Monadologia was written in France in 1714, ie, three hundred years ago, by the standards of the era and the expression of the thinker.
It’s a synthesis of his thoughts, and therefore it’s not an introduction to his way of thinking, on the contrary it presupposes, that the reader already knows that context and so passes directly into the action field. Leibniz’s units are fundamental, however, they have a degree of perfection that can be different, since there are the simple ones, those which have memory and those having cognition. In other words it’s not only minutely.
After one hundred years the concept of group appeared, thanks to the work of Galois, and we had to wait until 1854 to obtain the abstract definition of a finite group. And only in 1982 we’ve resulted in the classification of simple finite groups, through the most important collective works of the history of mathematics.
With this new tool, we realize that the concept of the simple is not simplistic. Also, even if the concept is fundamental, and even though it has an internal action, its structure is very substancial. In actual fact, we can build an Omadologia, following Leibniz’s initial steps and after holistically examining the issue of the unit through the group, in order to establish the uniqueness of the surface on a multiplicity of depth. In this way the combination of elements is involved, which although could be many, may produce one group only. And it’s the structure which is incorporating this combination.
Therefore, Omadologia indicates how the simple is complicated when it is fundamental, because the independent does not mean that there are not common elements in the new soul.