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- W3035650807 abstract "The notion of has sparked renewed interest in recent years, particularly in computer science and biology (neural network). However, this notion is usually interpreted in an extremely restrictive way: essentially linked to data processing, today networks are hybrid topologies in which star networks are generally interconnected via bus networks. These networks are, most often, hierarchical and regular, and each of their nodes can have an arbitrary number of child nodes. At the outset, however, the notion of network, introduced in 1936 by Belgian physicist Julien Pacotte, was quite different: more general and, at the same time, more constrained, it should also serve an ambitious objective: the reconstruction of mathematics from concrete empirical structures. Usually poorly commented on and poorly understood (especially by philosophers), it had no real posterity. In this article, we first try to clarify this notion of tree network in the sense of Julien Pacotte, which makes it possible to eliminate the bad interpretations to which this notion has given rise. To this end, we use the language and concepts of graph theory and formalize the main properties of these networks which, contrary to popular belief, are not, in general, trees. In a second part, we then try to follow and explain, step by step, how Pacotte intended, using concepts borrowed from projective geometry, to reconstruct all of mathematics from such a network." @default.
- W3035650807 created "2020-06-19" @default.
- W3035650807 creator A5073916836 @default.
- W3035650807 date "2020-06-09" @default.
- W3035650807 modified "2023-09-27" @default.
- W3035650807 title "Pacotte tree networks, graph theory and projective geometry" @default.
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