Structure, relations and singularities

N. Lygeros

Translated from French by Patrice Deloche and Nicolas Thouvignon

A way to approach a complex object is to characterize it by its singularities, without excluding however the self-referential aspect of this approach, because the singularities are considered as such only in relation to their neighborhood (local or even global); we might even say that a singularity out of context degenerates as far as meaning is concerned. Within this framework the complex object is generated by the singularities and their relations. The latter constitute a priori a structure independent from the former. The complexity of the object is therefore due to both of these entities. By applying this model to contemporary humanity we can notice on one hand that the singularities are more easily localized than before, and on the other hand that the structure made of their relations is in an inflationary stage. Indeed, this structure, which was so to say non-existent a few centuries ago, which arose through time in an indeterministic way or rather directly related to natural and human disasters so that we sometimes call renaissance its occurrence, which then emerged in the industrial era thanks to technique, and which was recreated afterwards under the threat of nuclear war, is now developing through the network. What is most remarkable about this phenomenon is that humanity can consciously participate in the elaboration of this structure. This new possibility brings humanity to an ontological reflection.

The operating mode of the singularities is before all algorithmic. At first sight it seems that we calculate quickly what we know, but experience shows that past a certain problem size, it is better to recalculate than to memorize (e.g. prime numbers). Moreover, and this even for objects of small size yet still complex, it is more interesting to know how to repeat a method that to remember the results. The algorithm includes logical information that disappears in the storing of the results. That is the reason why the singularities will have to think about the new use of memory by the system of relations. In other words, memory is a piece of humanity in intelligence.

If we consider now that the principle of recapitulation, which is valid within the framework of the biological evolution of man, can be transposed to the framework of the intellectual evolution of man – After all, does man not retrace humanity’s path to discover a new concept, a new abstraction? – this hypothesis leads us to think that the transformation of the functional mode of the singularities, considering the structure of their relations and its parallelization, will constitute a new class in the hierarchy of conceptual complexity and by the same token, will decisively increase the ontological complexity of the humanity entity.

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