Arborescent

Hydatica. Stem arborescent, jointed, branched; leaves long, linear.

In §1 we review the definition of the arborescent links and discuss a convention to inductively analyze these links. We also recall some facts about foliations. In §2 we show how to represent an oriented arborescent link L by a special type of tree called a candidate tree.

Robinia, with its center of distribution in the southern Alleghany region, is represented by two arborescent and one frutescent species in the Atlantic and by one arborescent species in the Pacific region.

We will say that the simplicial complex X is arborescent if we can obtain it by a sequence of Whitehead dilations starting from a point. This sequence can be non-locally finite. Also "arborescent" does not imply "collapsible" (R² for instance is arborescent). We will say that a 2-dimensional simplicial context X is almost arborescent if it can be obtained by a series of Whitehead dilations and of additions of 2-cells along their boundaries, starting from a point.

Gilles Deleuze criticizes the Chomsky hierarchy of formal languages, which he considers a perfect example of arborescent dualistic theory.

Deleuze and Guattari think, for instance, that metaphysics is an example of arborescent thinking, which is a model of thought like an erect tree, because it has been shaped by arboreal metaphors from the moment of its origin. They explain, "Arborescent systems are hierarchical systems with centers of significance (sic) and subjectification, central automata like organized memories. In the corresponding models, an element only receives information from a higher unit, and only receives a subjective affection along preestablished paths."

One [metaphor] in particular – the "arborescent schema" – emerges as perhaps the most long-held, dominant approach and way of thinking in such areas as philosophy, psychoanalysis, social criticism, and everyday life. It is, in plain, a tree-like representation of the world, which gathers concepts and images that encourage our minds to think of the world in terms of trees and their component parts. […] Deleuze and Guattari draw attention to the arborescent schemas in philosophy and other areas and show how these foundational ideas are rarely challenged, even though they limit the manoeuvrability of thought and violently organize all subsequent lines of inquiry. […] The problem with arborescent thinking is that thoughts must begin from the trunk, and refer back to it; they cannot pop up elsewhere.

René Descartes once likened the structure of philosophy to a tree: […] Building on Descartes' insight, Gilles Deleuze and Félix Guattari have argued that Western humanist tradition in general is modeled on a treelike structure, or what they term an "arborescent" structure. A tree organizes its parts according to a principle that arises out of its own interiority and self-sufficiency: it germinates from a solitary seed or acorn and shoots forth what will become its trunk. Its whole canopy of branches above is integrated downwards into this trunk, and all of its roots below are similarly integrated upward into the same trunk. Considered as a model of Western knowledge, the trunk of this arborescent structure represents human rationality. Rationality is the highest value in an arborescent structure because it is rationality that organizes and integrates all forms of knowledge into a unified, coherent system, […]